in a definite compound, but that there is a fraction of it, so to speak, to spare, we should only find Prout's law to hold good if we could analyse only one molecule of any compound, but, as in any analysis we can make, there must be many molecules, such atom of the molecules having a fraction of its affinity for the other to spare, these fractions would unite and hold in combination an extra number of the other atoms, not so firmly, perhaps, but still firmly enough to make the whole appear a definite compound on analysis, and this would affect the calculation for atomic weight. Thus, suppose two atoms of Cl 71 combine with one atom of Ca and still have part of affinity to spare, then 200 atoms of Cl would take up 101 atoms of Ca, and from this analysis we should make the atomic weight of Ca not 40 but 40·4.

=

=

40

4th. If chemical combination and solution are due to the same force, then solution will loosen the combination by spreading the affinity, and possibly there may be a re-arrangement of the soluble and solvent analogous to what is known to take place when two salts are mixed having different acids and bases. Hence the powerful effects of solution in promoting chemical reaction and electric conductivity.

5th. A point of practical importance may be noted regarding analysis. Many substances are added indefinitely to solution to render insoluble some body held in solution, which quantity is to be estimated. Now, if the way in which one substance renders another insoluble is by combination with the solvent, it is quite clear that if either too much or too little be added to the solvent, an error may be made in the analysis, as the whole of the precipitated body may

not be thrown down.

6th. A further investigation of this subject may throw some light on the manner in which the solubility of a solid in a liquid is related to the chemical composition of the two.

5. Note on the Surface of a Body in terms of a

Volume-Integral. By Professor Tait.

In § 25 of my paper on Green's and other Allied Theorems ("Trans. R. S. E." 1869-70) I gave the following relation between a

VOL. IX.

4 a

volume and a surface integral, the limits being determined by any simply continuous closed space :—

Vrds=Uv Tds.

If in this equation we assume (which is arbitrary) to be equal to Uv at every point of the surface, we have

T= = Uv=UVP

where PC is the (scalar) equation of the surface.

The equation

the limits being given by the equation of the surface.

6. On a White Sunbow. By Sir Robert Christison, Bart. As the phenomenon of a colourless rainbow, which was seen here in the forenoon of Thursday the 10th January, seems to be very rare, never having been witnessed before either by myself or by any of my friends to whom I have mentioned the subject, I beg to offer the Society the following description:

On my way that forenoon to the Botanic Garden, and arriving about a quarter-past eleven at the open view of the north at the bottom of Pitt Street, my attention was arrested by the appearance of a magnificent white bow, visible in its entire arch from end to end in the northern sky.

The air was frosty, very dry, uncommonly still, and in most quarters moderately clear. The smoke of the Old Town, however, rising high in the stillness above the ridge of the High Street to the south, obscured greatly the sun, which shone through the upper region of

the smoky veil without the slightest definition of its disc, white nevertheless, but so shorn of its brightness that I could easily look it in the face. I was unable to detect anywhere the slightest appearance of a shower or rain-cloud. The sun, my place of observation, and the summit of the arch, were in the same vertical plane. The summit of the arch reached about half-way to the zenith. The northern sky on which it was formed was somewhat hazy and grey in its lower region, but blue-grey, and tolerably clear in the region of the upper two-thirds of the arch.

In form the arch was identical with that of an ordinary rainbow, except that I thought it considerably broader; and its edges were in many places somewhat broken, so that it had exactly the appearance as if the sun had gathered in an arch a number of little woolly cloudlets. On minute search I could not detect any trace of colour from end to end. I asked the opinion on this point of two gentlemen whom I met at the lowest part of the road, at the wall between the road and the river, and one of them thought he could detect a very faint trace of colour over a small space at the extremity of the western limb. As the absence of colour, however, was the main phenomenon, I scanned the whole curve again and again with great attention, but could see no coloration anywhere.

At this lowest point of the road the edges of the bow were seen much more defined and sharp than when I first noticed it. As I advanced up the gentle slope from Warriston bridge towards the Botanic Garden, the summit of the arch began to break up, and to present the appearance of irregular flimsy cloudlets ascending in the sky above it. But before reaching the Garden gate the whole arch again formed an unbroken bow, and with both edges sharply defined like those of a common rainbow. At the same time a similar secondary arch had begun to form below the principal one, only half its width, and much closer to its neighbour than I remember to have seen in a double rainbow of the ordinary kind.

On returning homeward, about fifteen minutes later, I still observed, on issuing from the Garden, a sharply-defined colourless principal bow, and now a complete secondary one under every part of the bow visible from the roadway. As I proceeded southward every now and then the upper region of the bow seemed to be breaking up, and this appearance was very marked when I reached

Heriot Row, at the head of Dundas Street, the highest station in my walk. As I went westward along Heriot Row the breaking-up appeared greater and greater at every interruption of the street, which gave me a view of the northern sky; and when I reached the landing-place of my house, in Moray Place, from which, however, only the western half of the region of the bow could be seen, the whole appearances had vanished, and the sky was everywhere mottled with thin grey fleecy clouds, small and of irregular illdefined outline. I did not again look for it, but I understand it was partly seen by others so late as two P.M.

Various particulars, which it is unnecessary to mention, led me to suppose at the time that this colourless bow had some connection with the smoky column of air through which the sun's rays penetrated. But this supposition was put an end to by learning from my son that, when at Craigiehall, five miles west from town, in a smokeless atmosphere, he observed the bow distinctly about one o'clock. Its edges were never sharply defined so long as he noticed it. But it had no colour. Another gentleman present thought there was a limited blueness at one place. But my son satisfied himself that this was owing to a patch of blue sky behind, and he is sure that there was no colour at any part of the bow visible to him.

A better explanation has been suggested to me by Professor Tait, to whose theory I subscribe. But I leave it to himself to explain his views.

By Professor Tait.

I was unfortunate in not seeing the phenomenon till nearly 2 P.M., when I was on my way from College to the Observatory. It was then very faint, but I saw at once that it differed in a marked manner from an ordinary rainbow. From what I could see, I attributed its apparent whiteness to the greatly increased effective surface from which the light came. This was probably due to reflection from ice-crystals mixed with the drops of water in the thin strata of cloud which covered the whole sky. The sun's light was much dimmed, and the edge of its disc was very indistinct, as the clouds immediately round it, to the distance of at least a diameter, appeared nearly as bright as the disc itself. Hence this rainbow was probably very much less pure, while also much less bright, than the usual one.

This suggestion seems fully to explain all the appearances which I saw. It will be observed that both Sir R. Christison and Mr Buchan noticed the peculiar brightness of the clouds near the sun, so that it is probable that this explanation applies to the phenomenon as seen by them also. The peculiarities noticed in the position of the spurious bows (when seen) are of course dependent on the actual size, as well as the greater or less uniformity of size, of the drops which produced the rainbow; and these may well have been exceedingly variable as regards both time, locality, and height in the atmosphere.

[Added, April 8.]

I find that this nearly colourless rainbow is very easily reproduced in my class-room, when the sunlight employed to form a rainbow in fine spray is made to pass first through a large vessel with parallel glass sides, containing water and a little milk. This arrangement imitates very closely the circumstances of the 10th January.

By J. Christison, Esq.

I saw it first at Craigie Hall, five miles west of Edinburgh, about 11.30 or thereby. At first it did not make much impression, as the house front runs east and west, and I was standing at the front door, and consequently only saw half of the bow, and took it to be an accidental arrangement of the light clouds that covered most of the sky. By and by the idea of its being a rainbow struck me, and a move out from the house showed the full bow. I noticed it off and on for about an hour. Sometimes it was indistinct, but generally it was evident enough to attract attention at once. I did not, however, at any time see anything like clear definition of outline. There was always a sort of wavy indistinctness.

As to colour, I tried hard to convince myself I made it out, but without effect, and am quite satisfied there was none at any of the periods I looked at the bow. One of the party at Craigie Hall thought he made out colour, but on his pointing out the part where he thought it was visible I was satisfied that it was only a break in the bow, with a bit of very light blue sky showing through. I did not notice it after 12.30 or 12.45, as I was indoors.

It was pretty hard frost all the time. The only effect the sun had was to disperse a little of the hoar-frost, which was thick and heavy out there, and to make a few of the flat stones among the