144 



sent memoir. I have, however, excluded from the Tables, and I do 

 not in the memoir consider (otherwise than incidentally) the covariant 

 of the sixth order 0U, or the contravariant (reciprocant) FU. 



I have given in the memoir a comparison of my notation with that 

 of M. Aronhold. A short part of the memoir relates to the binary 

 cubic and the binary quartic, viz. each of these quantics has a cova- 

 riant of its own order, forming with it an intermediate olJ-f /3W, the 

 covariants whereof contain quantics in (a, /3), the coefficients of which 

 are invariants of the original quantic. The formula? which relate to 

 these cases are in fact given in my Fifth Memoir, but they are repro- 

 duced here in order to show the relations between the quantics in 

 (a, /3) contained in the formulae. As regards the binary quartic, 

 these results are required for the discussion of the like question in 

 regard to the ternary cubic, viz. that of finding the relations between 

 the different quantics in (a, /3) contained in the formulae relating to 

 the ternary cubic. Some of these relations have been obtained by 

 M. Hermite in the memoir " Sur les formes cubiques a trois indeter- 

 minees," Liouville, t. iii. pp. 37-40 (1858), and in that " Sur la Re'so- 

 lution des equation du quatrieme degre," Comptes Kendus, t. xlvi. 

 p. 715 (1858), and by M. Aronhold in his memoir already referred 

 to ; and in particular I reproduce and demonstrate some of the results 

 in the last mentioned memoir of M. Hermite. But the relations in 

 question are in the present memoir exhibited in a more complete and 

 systematic form. 



III. "On the Secular Change in the Magnetic Dip in London, 

 between the years 1821 and 1860." By Major-General 

 EDWARD SABINE, R.A., Treas. and V.P.R.S. Received 

 March 7, 1861. 



I propose in this communication to bring together and discuss four 

 determinations at different epochs, in which I have myself been either 

 directly or indirectly concerned, which have had expressly in view the 

 object which forms the title of the paper. 



Epoch 0/1821. The experiments on this occasion were made in 

 a part of the Regent's Park, then occupied as the nursery garden of 

 Mr. Jenkins : an unexceptionable locality in all respects, and far 



