Found it! I pointed out in my previous invisibility post that R.W. Wood attributes an early discussion of invisibility to Lord Rayleigh in his Encyclopædia Britannica article on optics; however, I couldn't find the quote after browsing Rayleigh's articles and wondered if Wood had miscited Rayleigh's work.
A bit of closer inspection, however, shows that I overlooked Rayleigh's comment, which was buried in a footnote in his article on geometrical optics (Encyclopædia Britannica, vol. 17 (1884, 9th ed.), 798-807), in what I would have considered an unlikely place, namely his discussion of achromatic object-glasses (p. 805). The footnote is as follows:
Even when the optical differences are not small it is well to remember that transparent bodies are only visible in virtue of a variable illumination. If the light falls equally in all directions, as it might approximately do for an observer on a high monument during a thick fog, the edge of (for example) a perfectly transparent prism would be absolutely invisible. If a spherical cloud, composed of absolutely transparent material, surround symmetrically a source of light, the illumination at a distance would not be diminished by its presence.
There are two different types of "invisibility" mentioned here. The first is the one that Wood covered in his paper: the hypothesis that an ideally transparent object, illuminated uniformly, will scatter light perfectly uniformly as well. In such a case, there is no externally observable way to distinguish between the presence or absence of an object, meaning that it is in effect invisible.
This is a rather limited and artificial interpretation of the idea of invisibility, because it is a result of a special type of illumination rather than a property of the object itself. Rayleigh's second type of invisibility is an even more specialized form: he suggests that if a perfectly transparent object (such as a fog) surrounds a uniformly radiating source of natural light, the transparent object will also transmit the light uniformly. Again, the effect is the same as if the object were not present, and it is in effect invisible.
Let us assume, similar to the previous post, that we have a very idealized source with only four directions of illumination. This source is surrounded by a perfectly transparent, though nonuniform, cloud. Rayleigh essentially argues that any light which is deflected from one path is perfectly balanced by light deflected into that path from elsewhere:
An observer outside of the cloud sees light radiating uniformly from all directions, and therefore cannot tell that a cloud is present:
A major difficulty with this notion of invisibility is that it really wouldn't work well in practice, even if it works in the idealized case. All objects, even highly transparent ones, absorb light to some degree. If we tried to surround an ordinary-sized light source with some sort of transparent cover, the cover would by necessity be rather large and would probably result in significant absorption of the light from the source. The result would be an object that radiates in a manner measurably different from the light source alone. Nevertheless, it is an interesting thought experiment.
Rayleigh himself apparently thought the idea was interesting, because soon after his optics article was published he elaborated upon it with an article entitled, "On the theory of illumination in a fog," Phil. Mag. 19 (1885), 443-446. In this short paper, Rayleigh attempts to 'illuminate' the effect of fog on a source of light using simple optical and thermodynamical arguments:
As a step towards a better understanding of the action of fog upon light, it seems desirable to investigate what the phenomena would be in the simplest case that can be proposed. For this purpose we may consider the atmosphere and the material composing the fog to be absolutely transparent, and also make abstraction from the influence of obstacles, among which must be included the ground itself. Conceive a small source of radiation, e.g. an incandescent carbon filament, to be surrounded by a spherical cloud, of uniform density, or at any rate symmetrically disposed round the source, outside of which the atmosphere is clear. Since by hypothesis there is no absorption, whatever radiation is emitted by the source passes outward through the external surface of the cloud. The effect of the cloud is to cause diffusion, i.e. to spread the rays passing through any small area of the surface (which in the absence of the cloud would be limited to a small solid angle) more or less uniformly over the complete hemisphere.
This paper does not explicitly discuss invisibility, but is clearly inspired by his earlier musings on the subject, concerning a light source contained in a perfectly transparent scattering object.
So it seems we can push the date of the first discussions of invisibility in physics to at least 1884, and attribute this first mention to Lord Rayleigh. It is not clear that this is the end of the story, however; Rayleigh's comments only appear in his encyclopedia article, which suggests that he either found the conclusions obvious or they were considered common knowledge at the time. In the latter case, it would seem that there would still be earlier articles to find on invisibility; I plan to keep searching!
I should note that Lord Rayleigh does use the word "invisibility" in one other earlier paper: "On the invisibility of small objects in a bad light," Camb. Phil. Soc. Proc. 4 (1883), p. 4. I think my heart skipped a beat when I first read the title! However, this paper is actually about vision: Rayleigh notes that his near-sightedness is much worse in dim light than it is in bright light, making small objects effectively invisible to him in the dark. This paper doesn't really count as a true invisibility reference.
For those who are interested, it is worth mentioning that almost all of Lord Rayleigh's scientific papers are available on Google books. This may have been a relatively recent development, as I recall searching fruitlessly for them some months back. The links are:
Only volume 5 (1902-1910) is unavailable.