381 



first becomes infinite in the case of a quantic of the order 7 ; the 

 number of irreducible covariants first becomes infinite in the case of 

 a quantic of the order 5. In particular, the formulae show that in 

 the case of a quantic of the order 5, or quintic, there are 4 irre- 

 ducible invariants of the degrees 4, 8, 12 and 18, respectively con- 

 nected by an equation of the degree 36 ; and that in the case of a 

 quantic of the order 6, or sextic, there are 5 irreducible invariants 

 of the degrees 2, 4, 6, 10 and 15 respectively connected by an 

 equation of the degree 30 ; so that the system of the irreducible in- 

 variants of a sextic is analogous to that of the irreducible invariants 

 of a quintic. The memoir concludes with a table of the covariants 

 of a quadric, a cubic, and a quartic, and of certain of the covariants 

 of a quintic. 



II. " On a Decimal Compass Card." By James M. Share, Esq., 

 Master R.N. Communicated by Rear-Admiral Smyth, 

 Foreign Secretary R.S. Received April 23, 1855. 



The mariners' compass-needle having of late years received great 

 improvements, I am of opinion it is high time the card, as at present 

 arranged, should take its place by the side of such things as are 

 superseded by others better adapted to the advancing spirit of the 

 times. 



I venture to make an attempt to innovate on an old custom, by 

 suggesting the substitution of a compass card containing thirty-six 

 points of ten degrees each every degree being one-tenth of a point. 



By the use of this card the mariner will avoid the constantly re- 

 curring trouble of turning degrees into points, and vice versd. 



The ship's course having been worked out in degrees, the devia- 

 tion and local attraction have but to be applied to adapt it to the 

 decimal steering card, thus rendering the " traverse table for 

 points" no longer necessary to those steering by it; the course 

 N. 35 E. being the same as " north three and a half points east," 

 &c. The same remark applies also to astronomical bearings, azi- 

 muths, amplitudes, &c. 



Should the decimal card be adopted, the old-fashioned method of 



