^{page 136 note *} To one taking this point of view Sylvester's paper “On Staudt's theorems ….” will be of interest. See Philos. Magazine, iv. (1852), pp. 335-345: or Collected Math. Papers, i. pp. 382-391.

^{page 137 note *} If we note that the first determinant can be written in the form

and the fourth in the form

light dawns at once, for the last three determinants of the identity are then seen to be principal minors of the first, and the identity itself to be a case of Jacbbi's theorem regarding a minor of the adjugate.

^{page 144 note *} In the Coll. Math. Papers §§ 1-6 are omitted, and §§ 7, 7', 8 are numbered §§ 6, 7, 8. The theorem of the original § 6 is incorrect.

^{page 146 note *} Already thus formed by Cayley in his first paper of all (1841).

^{page 146 note †} Observe that, although Cayley considers the two determinants of the previous case to be essentially distinct, the second is derivable from the first by multiplying the columns by abc, a, b, c respectively, and then dividing the rows by 1, bc, ca, ab respectively.

^{page 147 note *} Cayley fails to notice, however, that each of those is readily transformable into the second. Thus, taking his first form, we have only to multiply the 4th, 8th, 9th columns of it by a, and divide the 2nd, 4th, 7th rows by α, when we obtain a determinant which by mere permutation of the rows and subsequently of the columns becomes identical with the axisymmetric form.

^{page 153 note *} It would seem preferable to multiply the columns of A in order by xyz, x, y, z, the quantities just eliminated ; and then divide the rows by the multipliers 1, yz, zx, xy used in obtaining the set of equations. The advantage of this method would be still greater in the next case.

^{page 162 note *} The third, by reason of its central two-line minor which might have been , more specialised than a doubly axisymmetric determinant.

^{page 164 note *} Baltzer gives (p. 20) Cayley's determinant form for

placing in front of it what looks like a generalisation, namely

but is not really such. We can easily show that if a ₁, b ₁, c ₁ be multiplied and a ₂, b ₂, c ₂ be divided by x, y, z respectively, the determinant is unaltered; consequently it

^{page 165 note *} The new discriminant being

is easily seen to be equal to

and therefore to be separable into the two expressions referred to.