24 Mr. J. E. Drinkwater 07i Simple Elimination. 



the mass or quantity of metal employed in heterogeneous 

 thermo-magnetic combinations, I find that in the display of 

 the thermo-magnetic phasnomena of homogeneous bodies, the 

 quantity employed is an essential consideration ; for in several 

 of the metals, although no trace of thermo-magnetisni can be 

 detected in small pieces, its powers are promptly developed in 

 masses of considerable dimensions, and the laws of its phas- 

 nomena may be determined with precision. Zinc, when in large 

 masses, displays thermo-magnetic phcenomena in a very ex- 

 alted degree, but in small pieces hardly any trace of that 

 power is to be found. Copper is a still more striking instance 

 of the superior thermo-magnetic powers of large masses. 

 Those powers could not be detected in a few ounces of the 

 metal ; but in a mass weighing 60 or 70 pounds, they would 

 become very conspicuous. But a mass of copper of a hun- 

 dred weight, however heated, would not deflect a needle half 

 so far as it would be deflected by a single ounce of bismuth 

 or antimony. Yet, insignificant as these powers are in some 

 bodies, I have succeeded in detecting them in every metal of 

 which I had a sufficient quantity at command ; and I have no 

 doubt that they may be discovered in all the metals. 



Artillery Place, Woolwich. 



[To be continued.] 



II. On Simple Elimination. By J. E. Drinkwater, Esq."^ 



(] ). 'X'HE theory of elimination is intimately connected with 

 -■■ the general theory of the resolution of algebraical 

 expressions, and has engaged the attention of mathematical 

 writers in a corresponding degree. When the number of 

 equations and of unknown quantities is considerable, the labour 

 necessary for the extrication of any one of them becomes very 

 o-reat, even in the case of simple equations,— a case which is 

 perpetually recurring in physical investigations. The well- 

 known rule given for this purpose by Bczout will be found on 

 trial more laborious than it appears in its concise enunciation, 

 and no simple demonstration has yet been given of this or 

 any analogous general theorem. The investigation by Laplace 

 in the Memoires de V Acadcmie des Scie?ices, 1772, p. 2, which is 

 there only incidentally introduced, is both diffuse and difficult. 

 The following method of obtaining the final equations may be 

 easily identified with those of Laplace, Bezout, and Cramer, 

 although the coefficients are obtained in rather a different and, 

 as it is thought, a more convenient form. 



• Communicated by the Author. 



(2). Let 



