effective forces give bodily forces in the interior, the sum of whose moments about the axis of rotation is equal and opposite to the tidal frictional couple. The problem is thus reduced to finding the distortion of a sphere subject to bodily force equilibrated by surface action, and it is solved by Sir W. Thomson's method of finding the internal strain of an elastic sphere under like conditions, although here the bodily force has no corresponding potential function.

The solution shows that the distortion consists in a simple cylindrical motion round the axis of rotation, each point moving from east to west with a linear velocity proportional to the cube of its distance from that axis.

The distortion of the surface of the globe consists of a motion in longitude from west to east, relatively to a point in the equator, the rate of change of longitude being proportional to the square of the sine of the latitude.

Numerical calculation shows, however, that in the later stages of the earth's history (the development being supposed to follow the laws found in the paper on "Precession "), the distortion must have been very small. With a certain assumed viscosity, it is found that, looking back 45,000,000 years, a point in latitude 60° would lie 14' further east than at present. From this it follows, that this cause can have had little or nothing to do with the crumpling of geological

strata.

As, however, the distorting force varies inversely as the sixth power of the moon's distance, it seems possible that in the very earliest stages this cause may have had sensible effects. It is, therefore, noteworthy that the wrinkles raised on the surface would run north and south in the equatorial regions, with a tendency towards north-east and south-west in the northern hemisphere, and north-west and southeast in the southern one. The intensity of the distorting force at the surface varies as the square of the cosine of the latitude.

An inspection of a map of the earth shows that the continents (or large wrinkles) conform more or less to this law. But Professor Schiapparelli's map of Mars* is more striking than that of the earth, when viewed by the light of this theory; but there are some objections to its application to the case of Mars. If, however, there is any truth in this, then it must be postulated, that after the wrinkles were formed the crust attained sufficient local rigidity to resist the obliteration of the wrinkles, whilst the mean figure of the earth adjusted itself to the ellipticity appropriate to the slackening diurnal rotation; also, it must be supposed that the general direction of the existing continents has lasted through geological history.

The second question, considered in the first part, deals with the

*

"Memorie della Società degli Spettroscopisti Italiani," 1878, vol. vii.

non-rigid attachment of the permanent equatorial protuberance to the mean sphere. It is shown that the precessional and nutational couples will give rise to certain tides of the second order (varying as the tidegenerating force multiplied by the precessional constant), but not to any secular shifting of the surface over the interior, as has been supposed would be the case by some writers.

II. Distribution of Heat generated by Internal Friction, and the secular cooling of the Spheroid.

In the paper on "Precession" it was shown by the theory of energy, that a very large amount of heat might have been generated inside the earth by friction, but the investigation gave no indication as to its distribution. The problem is here considered by finding the amount of work done per unit of time on each element of the interior in the course of the tidal distortion.

The aggregate work done on the whole globe is found to be the same as that given by simple considerations of energy. The rate of work is equal to the tidal frictional couple multiplied by the relative angular velocity of the moon and earth; but this simple law arises out of a complex law of internal distribution. By far the larger part of the work done, or heat generated, is found to be in the central portion.

My first impression was that the large amount of heat, which might be generated, would serve to explain in part the observed increase of underground temperature; but the solution of a certain problem concerning the cooling of an infinite slab of rock 8,000 miles thick, in which heat is being generated according to a certain law of distribution, shows that the frictional heat could not possibly explain a rate of increase of underground temperature near the earth's surface of more than 1° F. in 2,600 feet.

It follows, therefore, that Sir W. Thomson's investigation of the secular cooling of the earth cannot be sensibly affected by this cause.

III. The Effects of Inertia in the Forced Oscillations of Viscous, Fluid, and Elastic Spheres.

In the theory of tides used hitherto the effects of inertia have been neglected. It was, however, shown that this defect in the theory could not have an important influence, unless the frequency of the tides was much greater than that of those generated by the moon at the present time. Nevertheless it was desirable to determine what the effect of inertia actually is.

This part of the present paper contains a second approximation to the theory of tides of a viscous spheroid.

VOL. XXVII.

P

The first approximation, being that given in the paper on "Tides," is here used to give a value to the terms introduced in the equations of motion by inertia. Physically the terms so introduced are equivalent to an addition to the bodily force which tends to produce the tidal distortion. The problem is then treated by a process parallel to that used by Sir W. Thomson in his statical problem concerning the strain of an elastic sphere. The analytical investigation is long and complicated, and it will here suffice to state the result with regard to the form of the tidal protuberance, when the tide-generating potential is of the second order of harmonics. It is as follows:-If a be the

radius, w the density, g mean gravity, and g=29, v the "speed" of

η

5a

the tide, the alteration of phase; so that ŋ÷v is the "lag," and v the coefficient of viscosity.

And the height of tide is equal to the equilibrium tide of a perfectly fluid spheroid multiplied by

This shows that the defect of the first approximation was such that for a given speed, the lag is a little greater, and for a given lag, the height of tide is a little greater than was supposed.

It is then shown that this correction to the theory of tides will scarcely make any appreciable difference in the results of the integration, by which the secular changes in the configuration of the earth and moon, were found in the paper on "Precession ;" and especially that it makes no difference as to the critical relationship between the month and day, for which the rate of change of obliquity vanishes. The most important influence of the new theory is on the time, and it appears that the time occupied by the changes, above referred to, is overstated by perhaps th part.

which occurs in 5%. The discrepancy fact that in approaching

or

75 150°

A comparison is then made of the preceding theory with that of the forced vibrations of a fluid sphere. This shows that when ʼn is zero (ie., when viscosity graduates into fluidity), the the above expressions should properly be between the 79 and 75 is explained by the the problem of fluidity from the side of viscosity, we suppose in the first approximation, that the motion of the interior of the sphere is vortical, whereas in reality it is not so.

In conclusion, it is proved that analysis, of almost identically the same character as that for the problem of the viscous sphere, is applicable to the case of an incompressible elastic sphere, and that inertia has the effect of increasing the ellipticity of the tidal spheroid, as given

by Sir W. Thomson's statical theory, in the proportion of 1+

79v2 150(r+g)

to unity, where v is the speed of the tide, and r is the quantity defined

in Thomson and Tait's Nat. Phil., § 840 (28), viz.,

cient of rigidity.

19

5wa

X the coeffi

The last part of the paper contains a discussion of results, and a non-mathematical summary of what precedes.

IV. "On the Influence of Light upon Protoplasm." By ARTHUR DOWNES, M.D., and THOMAS P. BLUNT, M.A. Oxon. Communicated by J. MARSHALL, F.R.S., Surgeon to University College Hospital. Received October 9, 1878.

This paper is in continuation of, and supplementary to, a previous communication* in which we recorded the first part of an investigation on the effect of light upon Bacteria and other organisms associated with putrefaction and decay. The chief conclusions to which those observations led us were briefly as follow:

:

(1.) Light is inimical to, and under favourable conditions may wholly prevent, the development of these organisms; its action on Bacteria being more energetic than upon the mycelial (and torulaceous) fungi which are prone to appear in cultivation-fluids.

(2.) The fitness of the cultivation-fluid as a nidus is not impaired by insolation.

We found also that tubes, containing a cultivation-fluid and plugged with cotton-wool, when removed to a dark place after exposure to the sun for a sufficient period, remained perfectly clear and free from organisms for months, and we naturally thought that the contents had been reduced to permanent sterility. The following facts, however, compel us to suspend for the present our conclusions on this point. Of the many tubes which we insolated last year we finally kept only three. Two of these-containing Pasteur solution of the composition given in our former paper-had been exposed to sunlight for three weeks in June, 1877; the third tube contained urine and had been insolated for about two months-commencing July 26th. In each case corresponding tubes which were covered with laminated lead, so as to exclude light, had swarmed with Bacteria in the course of two or three days, but the three tubes of which we speak not only were perfectly pellucid at the time they were removed from the light but, although kept in a warm room, remained clear all through the winter. On February 25th, 1878, however,-eight months after we had placed "Proc. Roy. Soc.," vol. xxvi, p. 488.

them in darkness-the two tubes of Pasteur solution each contained several tiny specks of mycelium.

One of the two was on this again exposed to sunlight, and in it the mycelial development was at once stopped; the other tube was left in the dark and the fungus gradually grew till it filled the whole space of the liquid, which on microscopical examination was found to contain no other organisms. The tube of urine remained clear till July 15th, 1878,-nearly ten months after incasement, on which date two specks of mycelium appeared, and subsequently developed as in the previous case. No Bacteria could be seen on examination with an immersion". It is noteworthy that a companion tube to this which was incased after six days of insolation had developed a growth of mycelium in three or four days.

It would seem that in the three tubes above mentioned Bacteria, or their "germs," had been either wholly destroyed or reduced to so low a state of vitality that they were unable to develope in the fluids in question; while it is evident that the spores of the mould which at length appeared, unless they had been accidentally shaken down from the cotton-wool plugging the tubes, had undergone some change which reduced them to a condition of torpidity from which in process of time they emerged. Such a condition, we may perhaps conceive, might be brought about by any influence causing thickening of the cell-wall of the spore. We hope at a future time to offer some further evidence on this question of revival of dormant germs, which is, we think, of much interest.

From a very early period of our inquiry we have set ourselves to the task of investigating the intimate nature of the remarkable action of light upon these organisms, and we have arrived, as we believe, at a satisfactory solution of the problem, but in the first place it will be well to describe some preliminary experiments.

An interesting point to be determined was the question,-with what part of the spectrum is this property of light associated.

The observations made by us last year indicated that the rays of greatest refrangibility were the most active, but the experiments then made did not warrant any definite conclusions as to the part played by rays of lower refrangibility.

The method employed in the more recent experiments was similar to that described in our former paper :

Small test-tubes containing the cultivation-fluid were suspended in deep narrow boxes made of garnet-red, yellow, blue, and ordinary glass respectively. Each box held about six test-tubes, and corresponding series were incased in laminated lead.

A spectroscopic examination of the glass of which these boxes were constructed showed that the yellow and blue were far from being monochromatic. The red was an excellent glass for the purpose.