forms which I have considered in my memoir on the Calculus of Functions published in the Philosophical Transactions for 1862, in which the general solution of the equations

4(x)−x(x)ø {a+bx}=F(x),

where is the unknown function, has been obtained.

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I. "Comparison of Mr. De la Rue's and Padre Secchi's Eclipse Photographs." By WARREN DE LA RUE, F.R.S. Received August 8, 1864.

I have stated, in the Bakerian Lecture read at the Royal Society on April 10, 1862, that the boomerang (prominence E)* was not depicted on Señor Aguilar's photographs. This is true of the prints which came into my hands in England. A visit to Rome in November 1862, however, afforded an opportunity for the examination of the first prints which had been taken in Spain on the day of the eclipse, previous to those printed off for general distribution by Señor Aguilar. I was agreeably surprised to find that the photograph of the first phase of totality showed not only this prominence very distinctly, but also other details, presently to be described, which were quite invisible in Señor Aguilar's copies. I had in fact experienced some difficulty in comparing measurements of my photographs with those of Señor Aguilar's, on account of the indistinctness (woolliness) of the latter, which I have attributed to Padre Secchi's telescope not having followed the sun's motion perfectly. A careful examination of the prints in Padre Secchi's possession has, however, convinced me that this was not the case during the period of exposure of the first negative; for I have been able to identify with a magnifier many minute forms which could only have been depicted by the most perfect following of the sun's apparent motion. For instance, my statement that the prominence H (the fallen tree) was not seen from having been mixed up with the prominence G, is not applicable to Padre Secchi's copy of the first phase of totality, for in it every detail of the fallen tree can be made out.

On expressing to Professor Secchi my surprise at the great discordance between the copy of the first phase of totality sent to me by Señor Aguilar and that of the same phase in his possession, I was informed that after a few positive prints had been taken from the then unvarnished negative, it was strengthened by the usual photographic process with nitrate of silver. This I look upon as an unfortunate mistake, as the images of the prominences were increased and their details hidden, and the beauty of the negative for ever lost.

It occurred to Padre Secchi and myself that although there was no hope * See Index Map, Plate XV. Phil. Trans. Part I. 1862.

of procuring more satisfactory prints from the original negative of the first phase of totality, yet some advantage would arise from taking an enlarged negative from the positive print in his possession, although it could not be expected to yield as perfect an impression as might have been obtained by enlarging from the original photograph. The enlargement has been successfully accomplished in my presence; and although Professor Secchi will take such means as he may, think proper to make known the results of comparisons he may make between my photographs and his own, it will not be out of place for me to add a few remarks by way of appendix to my paper.

Taking the prominences in the order in my index map, Plate XV. :Prominence A (the cauliflower or wheatsheaf) has the same form in Padre Secchi's photograph as in mine. It extends considerably less in height above the moon's edge in this copy than in that printed off from the strengthened negative (Señor Aguilar's copy); the bright points of the two branching streams which issue from the summit towards the North are well depicted in the Secchi photograph, but not the fainter parts.

There exists a faint indication of the minute prominence B in the S. photograph.

The convolutions of the prominence C (the floating cloud) are seen in the S. photograph, and its form coincides absolutely with that of mine; it is a little nearer the moon's edge at the point c, probably because the telescope was uncovered relatively a little later than at Rivabellosa.

The prominence D cannot be clearly traced in the S. photograph. The boomerang E is distinctly visible in the S. photograph; the point e is apparently prolonged; but this I attribute to an accidental photographic stain, for the bright part e' can be well made out.

The long prominence F cannot be made out in the S. photograph, probably from the cause explained in reference to C.

The fallen tree (H in the S. photograph) corresponds in its minutest details with its picture in my own. The articulated extremity h, the round points h' h", the point h", and the connecting branch joining it with the stem are clearly seen.

The prominence G from gto g' corresponds precisely in the S. photograph with its image in my own, and a dark marking near g also is seen; the narrow portion of this prominence, from g to the point immediately below h, is not seen in the S. photograph.

The prominence I (the mitre) agrees in form in the S. photograph with its image in my own, even the faint point i is there seen. This prominence in the S. photograph extends further from the edge of the moon than in mine; and whereas in my photograph the convex boundary next the moon is cut off by the moon's limb, in Padre Secchi's the convex boundary is complete, and hence in all probability the prominence I presented another case of a floating cloud.

About midway between G and I there is a small round prominence visi

ble in the S. photograph not seen in mine, which may be accounted for from our different positions in respect to the central line of the eclipse.

Between I and K, at a distance from I equal to about two-thirds the angular interval, there is in the S. photograph a prominence consisting of two round dots, which extend beyond the moon's limb to precisely the same extent as the prominence K protrudes in Professor Secchi's photograph beyond the moon's limb in excess of what it does in my own.

The prominence K has precisely the same form in every respect in the S. photograph as in mine, so far as mine shows it; but on account of parallax, more of it is seen in the S. photograph than in mine.

Beyond K is another prominence, visible in the S. photograph about 17° distant from K, a small round prominence which could not have been visible from my station.

Of the remaining prominences, L, M, N, O, P, Q, R, none were visible at the epoch of the photograph.

In conclusion, the photographic images of the prominences, so far as they are common to the two photographs taken at Miranda and Desierto de las Palmas, accord in their most minute details. The photographs must, from the difference of position of the two stations, have been made at an absolute interval of about seven minutes; and this fact, while it strongly supports the conclusion that the protuberances belong to the sun, at the same time shows that there is no change in their form during an interval much greater than the whole duration of an eclipse.

II. "On Drops." By FREDERICK GUTHRIE, Esq., Professor of Chemistry and Physics at the Royal College, Mauritius. Communicated by Professor STOKES, Sec. R.S. Received July 15, 1864. In the following investigation, the word drop is used in a rather more definite sense than that which is usually attached to it.

In common speech a drop signifies any mass of liquid matter whose form is visibly influenced towards the spherical by the attraction of its parts, and whose sensible motion or tendency is towards the earth. This definition both includes drops with which we are not here concerned, and excludes others which we shall have to consider; for we shall have to measure the size of drops; and it can only be of avail to measure the size of such drops as are formed under fixed and determinable conditions.

How many drops, according to the usual scope of the term, are formed under indefinite conditions. For instance, a rain-drop depends for its size upon such circumstances as the quantity of vapour at the time and place of its formation, the tranquillity and electrical condition of the air, its rate of motion, the number and size of the drops it meets with in its course, &c., all of which are fortuitous, or, at least, immeasurable conditions.

With such drops we have here nothing to do, but only with those which are formed under fixed circumstances. On the other hand, we

shall have to consider drops which move upwards*. Drops of this kind are so seldom met with that no distinguishing name has been given to them. We shall find it convenient to include them in the general term drop, though it may appear at first inapplicable to them.

Without attempting to give an exhaustive definition, it will be sufficient to define a drop as a mass of liquid collected and held together by the attraction of its parts and separated from other matter by the attraction of gravitation. This definition will exclude such drops as those of mist or rain, and will include the upward-moving drops mentioned above.

It follows that the size of a drop may depend upon and be influenced by variation in

(1) The self-attraction and cohesion of the drop-generating liquid;
(2) Its adhesion to the matter upon which the drop is formed;
(3) The shape of the matter from which the drop moves;

(4) The physical relation of the medium through which the drop moves, on the one hand, to the liquid of which the drop is formed, and on the other, to the matter on which it is formed;

(5) The attraction of the earth, or gravitation, upon the drop-forming liquid and upon the medium, as influenced by their respective and relative densities, and by variation in the attracting power of the earth.

In order to study systematically the influence which each of these factors exerts, each must be varied in succession while the others remain constant.

Denoting the three states of matter, solid, liquid, and gaseous, by the symbols S, L, G respectively, and considering the symbols in the order in which they are written to denote respectively the matter from which the dropping takes place, the drop and the medium, we get a convenient notation.

As we are speaking at present exclusively of liquid drops, L must always hold the middle place in the symbol.

Of the eight symbolically possible variations,

(2) (3) (4) (5)

(6) (7) (8)

(1) SLS, SLL, SLG, LLS, LLI, LLG, GLS, GLG, (1), (4), and (7) are physically impossible on account of the superior cohesion of solids over liquids, (6) and (8) are physically impossible on account of the superior density of liquids over gases.

SLL, SLG, and LLL are therefore the only cases we have to consider. That is,

* Owing to the numerical preponderance of downward-moving drops, we are prone to associate the ideas of "drop" and "down." How far I may be justified philologically in using the expression "drop up," must depend upon the relative primitiveness of the noun and verb "drop." Once for all, I beg permission to use the term drop in this more extended sense.

Of course, in the absence of positive levity, an upward drop can only be caused by the downward motion of the medium in which the drop moves.

SLL, from a solid a liquid drops through a liquid.
SLG, from a solid a liquid drops through a gas.

LLL, from a liquid a liquid drops through a liquid.

Of these three cases, two, SLL and LLL, may be inverted; that is, the motion of the drop may be towards or from the earth. The gravitation of the drop may be greater than and overcome the gravitation of the medium, the drop descends; or the gravitation of the medium may overcome that of the drop, the drop ascends. The case SLG cannot be inverted, because, at all events, at the same pressure every known gas is lighter than every known liquid.

It will be convenient to consider the case SLG first, because instances of it come more frequently under our notice than of the other two, and because it will be convenient to consider together those cases which are capable of inversion.

As we are considering the physical aspect of the question, we will only discuss those cases where no chemical action takes place between the terms, and where either no solution takes place, or where it is so small as to be negligible, or of such a kind as to admit of experimental elimination. This limitation of course excludes a vast number of combinations, but it must be made in order to study the purely physical and definite influences which determine the size of a drop.

SLG. From a Solid a Liquid drops through a Gas.

The variable factors are

1. The self-attraction and cohesion of the liquid:

A. Dependent on its purely chemical constitution.

B. Dependent on the proportion and physical relation between its heterogeneous parts, when a mixture.

C. Dependent on temperature.

2. The adhesion between the solid and the liquid:

A, B, C as in 1.

D. Dependent upon the shape of the solid.

3. The adhesion of the gas to the solid.

4. The adhesion of the gas to the liquid..

The factors 3 and 4 may be neglected, as we shall at present only consider the case where the gaseous medium is air at the ordinary barometric pressure.

One of these factors, namely temperature, though varying in different cases, may be supposed in the same case to be the same for the different kinds of matter present. Another factor in the same predicament is the locally constant gravitation at the place where the dropping occurs. Lastly, a condition of great influence is the length of the time-interval between the successive drops. This interval we shall call, for brevity, the growth-time, and denote by gt.

If the above conditions are exhaustive, we may assert that a drop of