nablan.

1837 W. R. Hamilton in Trans. Royal Irish Acad. 17 Science 236 Considering x as a function ψ of a new variable o′ and performing any operation ∇′ with reference to the latter variable, ∇′fψ(o′) = ∇′f(1 + Δ) (ψ(o′))^o.

1847 Proc. Royal Irish Acad. 1845–7 3 291 The following..general characteristic of operation i^d/ _dx + j^d/ _dy + k^d/ _dz = ◁, in which x, y, z are ordinary rectangular coordinates, while i, j, k are his [sc. Hamilton's] own coordinate imaginary units, appears to him to be one of great importance in many researches.

1847 W. R. Hamilton in Philos. Mag. 31 291 In the paper designed for Southampton..the characteristic was written ∇; but this more common sign has been so often used with other meanings, that it seems desirable to abstain from appropriating it to the new signification here proposed.

1853 W. R. Hamilton Lect. Quaternions vii. 610 Introducing, for abridgment, as a new characteristic of operation, a symbol defined by the formula ◁ = [etc.].

1870 J. C. Maxwell Let. 7 Nov. in C. G. Knott Life P. G. Tait (1911) iv. 143 Dear Tait, ∇ = i^d/ _dx + j^d/ _dy + k^d/ _dz... What do you call this? Atled?]

1870 W. R. Smith Let. to P. G. Tait 10 Nov. in MS Cambr. Univ. Libr. Add. 7449 C. 78 My dear Sir, The name I propose for ∇ is, as you will remember, Nabla... In Greek the leading form is ναβλᾰ... As to the thing it is a sort of harp and is said by Hieronymus and other authorities to have had the figure of ∇ (an inverted Δ).

1870 J. C. Maxwell Let. 14 Nov. in C. G. Knott Life P. G. Tait (1911) iv. 144 If Cadmus..had consulted the Phoenician Professors about a name for it there can be no question that Nabla would have been chosen.

1884 W. Thomson Notes Lect. Molecular Dynamics & Wave Theory of Light at Johns Hopkins Univ. (MS) x. 112 I took the liberty of asking Professor Bell..whether he had a name for this symbol ∇²; and he has mentioned to me nabla, a humorous suggestion of Maxwell's. It is the name of an Egyptian harp, which was of that shape.

1893 Philos. Trans. 1892 (Royal Soc.) A. 183 431 Physical mathematics is very largely the mathematics of ∇. The name Nabla seems, therefore, ludicrously inefficient.

1911 C. G. Knott Life P. G. Tait iv. 145 It was probably this reluctance on the part of Maxwell to use the term Nabla in serious writings which prevented Tait from introducing the word earlier than he did.

1939 D. E. Rutherford Vector Methods iv. 50 A convenient method of writing grad ϕ is ∇ϕ, where ∇ (pronounced ‘nabla’) is defined as the vector operator ∇ ≡ i^∂/ _∂x + j^∂/ _∂y + k^∂/ _∂z.

1964 S. Simons Vector Anal. v. 69 If we define a vector differential operator ∇ (called ‘del’ or ‘nabla’) by ∇ = i(∂/∂x) + j(∂/∂y) + k(∂/∂z), then it follows..that grad V = ∇V.

1989 VNR Conc. Encycl. Math. (ed. 2) 479 The three differential operators grad, div, curl can be written in terms of a single operator, the nabla operator.

1995 C. Sagan Demon-Haunted World (1997) xxiii. 363 The ‘dot product’ and the ‘cross product’ after the nablas are statements of two different kinds of spatial variation.