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FIG. 30.-FOG STRATUM; CLEAR ABOVE AND CLOUDY BELOW.

Will dissipate in about three hours. Fog stratum as shown here is about 20 miles square. The elevation of the under surface is 1,000 feet; the thickness of the stratum is between 400 and 800 feet.

In Von Bezold's third paper on the "Thermodynamics of the atmosphere" (see Mechanics of the Atmosphere, pp. 257-288) the effect of mixing different air masses is considered. If two masses of saturated air at 0° C. and 20° C., respectively, and at 700 mm. pressure are thoroughly mixed, the greatest amount of rainfall that can occur is 0.75 gram per kilogram of air and water vapor. The temperature of the mixture will be 11° C. (52° F.). The warmer mixture would have yielded the same amount of rainfall by raising it 310 meters or cooling it 1.6° C. by elevation and 0.8° C. by contact.

Direct cooling by contact or radiation is shown by Von Bezold to be more efficient as a cause of rainfall than cooling by mixture, but in the production of fog it is probable that cooling by mixture (except in the case of ground fogs) is the most important factor to be considered. It is to be noted that reverse pressures should also be studied, for perhaps a close watch upon the conditions prevailing when fog is rapidly dissipating might conversely throw light upon the order and relative importance of the three ways of cooling, viz, mixture, expansion, and radiation.

Von Bezold's deductions may be thus summarized: More vapor condenses when a stream of air and vapor at low temperature impinges on a mass of warmer air than with reversed conditions. Ocean fogs as a rule form when cool air flows over warm, moist surfaces, but in the case under discussion, where the ocean surface temperature is 13° C. (55° F.) and the air temperature may reach 27° C. (80° F.), it is evident that the above does not hold. It is more probable that condensation is the result of the sharp temperature contrasts at the boundaries of certain air currents having different temperatures, humidities, and velocities, and that the contours of the land play an important part in originating and directing these air currents. The summer afternoon fogs of the San Francisco Bay region, then, are probably due to mixture more than radiation or expansion. The winter tule fogs of the Sacramento and San Joaquin valleys are probably pure types of radiation fog, where the process of cloud building is from the cooled ground upward. Occasionally in summer, when the warm air has been pumped out of the valleys and there is rapid radiation, ground fog forms. An illustration of this is given in fig. 22, Plate I, where fog covers a number of valleys. Summer sea fog is shown in fig. 23, Plate II, and, as said above, is probably due to mixture. The wave motions or Luft Wogen of Von Helmholtz are shown in fig. 24, Plate II, and also the surgings or splashings, where a certain condensation results from the mechanical uplifting.

In several papers presented to the Royal Academy of Sciences of Prussia, Prof. H. von Helmholtz has discussed the conditions which must occur in the atmosphere where strata of different densities lie close together, with particular reference to the billow and wave effects near the limiting surfaces of the strata.

"It apppars to me not doubtful," says Helmholtz, "that such systems of waves occur with remarkable frequency at the bounding surfaces of strata of air of different densities, even although in most cases they remain invisible to us. Evidently we see them only when the lowest stratum is so nearly saturated with aqueous vapor that the summit of the wave, within which the pressure is less, begins to form a haze."

It is probable, as Helmholtz states, that conditions favorable for the origin and propagation of air waves often exist, but with the exception of certain cloud forms it is seldom that the meteorologist has an opportunity to see this wave action clearly defined. It therefore seems of importance to present a few photographs showing the actual wave effects produced probably by the sharp contrasts of air currents of different densities in the vicinity of Mount Tamalpais.

It is thought that in the photographs of fog billows (Plates III and IV) there is evidence of the movement of rectilinear waves propagated, with little change of form and velocity, along the bounding surfaces of the different air strata.

With a wind velocity of 10 meters per second, which nearly corresponds with the mean velocity of the inflowing colder current (the average summer afternoon velocity of the wind through the Golden Gate is about 22 miles per hour), the wave length, A, is determined by Von Helmholtz to be about 900 meters (2,950 feet). The wave lengths shown in the various fog photographs herewith are of corresponding magnitude and vary, it is estimated, from 100 to 2,000 meters. Helmholtz states further:b

"Since the moderate winds that occur on the surface of the earth often cause water waves of a meter in length, therefore the same winds acting upon strata of air of 10° difference in temperature maintain waves of from 2 to 5 kilometers in length."

Equations for the velocity of propagation and the diminution of the speed with a change of the depth of the lower stratum and a discussion of the energy of the waves are given for special cases. It is also pointed out that the elevations of the air waves can amount to many hundred meters, and that precipitation could thus be mechanically brought about. The same wind can excite waves of different lengths and velocities, and the interference and reenforcement may perceptibly modify the wave form. One of the processes by which waves of great height can be formed is thus pointed out by Helmholtz, namely, where two wave summits of different groups of waves reenforce each other. The wave height may be so great that foaming is produced. Such long and deep waves may have a bearing on the explanation of certain local and nonperiodic disturbances.

The demonstrated existence of these air billows and waves is important also in connection with the transmission of other air waves. It is well known that sound waves are reflected and refracted in a marked degree in the vicinity of fog banks, fog walls, and fog billows. The inaudibility of fog signals from sirens is one of the greatest sources of danger and anxiety in navigation. Any increase in our knowledge of the dispersion and aberration of these fog signals will be hailed with joy by many thousand travelers. In the vicinity of San Francisco, as evidenced by the a See Abbe's Mechanics of the Earth's Atmosphere, p. 94.

See Mechanics of the Earth's Atmosphere, p. 103.

series of photographs accompanying these papers, the opportunities for studying the general aberration of sound waves in fog are excellent. It is our earnest hope that in due time some experimental work in this direction may be undertaken at the observatory on Mount Tamalpais. Some very strange effects have already been noticed with regard to the noise of a train when traversing different air strata.

Zones of audibility appear to be quite sharply marked, even after making allowance for the many canyons and "mesas" (tablelands). On foggy days these zones are greatly modified. In addition to changes in density and temperature which sound waves would experience, there are changes due to the movement of the sound-conveying medium. The strong air currents moving toward the listener increase the frequency of vibration and raise the pitch; conversely the air currents moving away from the listener flatten the note.

There have been several instances on nights without fog where ordinary sounds have been heard distinctly a distance of nearly two miles. On other occasions it has been possible to obtain echoes from hills distant one-half mile or more when the intervening valley was covered with fog. The echoes could not be heard when the fog was absent.

The accompanying photographs may throw light upon the much-discussed question of the abnormal aberration of fog signals. It will be remembered that Prof. Joseph Henry, who for twelve years served as chairman of the Light-House Board, thought that the wind played a more important part in the abnormal aberration of sound waves than the so-called acoustic clouds described by Professor Tyndall. It is probable that up to a certain point both explanations may hold, but the wind is seemingly the more active factor in most cases. Sound moving with the wind is refracted downward and moving against the wind refracted upward. a

From the great mass of conflicting evidence it appears that a homogeneous atmosphere without the internal stream lines (see reference to this under "Air drainage," in previous pages) conveys sound waves very well; but this is not the usual condition. Under normal conditions the mass of air within a mile or two of a light-house and extending upward half a mile is neither still nor homogeneous. One of the main purposes of the accompanying fog photographs is to show the stratification, faulting, and upheaval effects due to differences of temperature and density caused by extensive and rapidly moving currents. Of course the aberration of audibility of fog signals due to changes of the sound-conveying medium is not to be confounded with the aberration in audibility due to topographical features and the normal reflection and refraction of sound waves. Probably within a short distance of every light-house there are zones or points of inaudibility due to the latter causes. An excellent illustration of this can be found in a paper on Fogs and Fog Signals of the Pacific Coast, by Ferdinand Lee Clarke. It is there shown that the sirens around the Golden Gate and in San Francisco Bay are inaudible at certain points. Here there is an interference of sound waves due to numerous natural reflections.

It has been suggested that if the fog signals at Lime Point and at Point Bonita were properly attuned a resulting harmonic might be heard at certain points instead of the weakened noise now heard. We need measurements of the energy producing the air pulsation, the proportionate energy reaching the ship or given point, and the rate of expenditure with different conditions of density and air movement. By the employment of suitable resonators the pulsations reaching the ship might be more easily detected. With the introduction of etheric telegraphy it would almost seem practicable to obtain by this same principle of resonance electromagnetic signals, and by comparing the time intervals between these and the sound waves in air or transmitted through water the distance apart of the vessels or the distance from the shore might be determined within a few feet.

The velocity of sound, it is generally stated, is within wide limits practically independent of both intensity and pitch. In dry air at 0° C., according to Rowland, the velocity of sound propagation is 331.78 meters (1,090 feet) per second. In water vapor at 10° C., according to Masson, the velocity is about 402 meters (1,318 feet) and at 96° C. 410 meters (1,345 feet) per second. In water at 10° C. the velocity is about 1,435 meters (4,708 feet), in copper about 3,560 meters, and in glass from 5,000 to 6,000 meters.

The velocity is proportional to the square root of the absolute temperature, as given by the formula:

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The velocity of sound propagation in dry air is therefore about 37 times more rapid than that of the average summer afternoon winds (20 miles per hour), which blow through the Golden Gate with such regularity and which are the prime disturbing factors in the circulation of the air in this vicinity. The question of refraction of sound in free air has been independently studied by Stokes," Taylor, Henry, Tyndall," and Reynolds, and many of the puzzling phenomena connected with the aberration of sound can be demonstrated to be caused by the bending of the sound beams in traversing air strata of varying temperatures and motions. The most efficient cause of loss of audibility is wind. The loss is not due to an actual retardation of the sound waves by the movement of the air so much as to a refraction of the wave front upward from the earth. Sound traveling with the wind is bent downward and traveling against the wind is bent upward. Knowing this, we are able, by lifting the position of the hearer,

a Report British Association, 1857.

b Smithsonian Report, 1875.

e Smithsonian Report, 1877.

Philosophical Transactions, 1874.

t

Philosophical Transactions, 1876.

sometimes to make sound audible against the wind. Thus Henry shows that a sound moving against the wind, inaudible to the ear on the deck of a vessel, could be heard at the masthead. Reynolds's experiments even more conclusively demonstrate the bending of the wave front downward as a rule when moving with the wind and upward when moving against the wind.

The accompanying photographs, Plate V, figs. 27 and 28, show air strata moving with varying velocities. As a rule the upper currents have the greater velocity, but not infrequently this condition is reversed. In such cases audibility should be favored even by an opposing wind, and this is sometimes found to be the case. Thus far we have alluded only to the refraction of the wave fronts due to varying air velocities; but the varying temperatures of the different air masses will also affect the relative audibility. Reynolds instances a marked case, where, owing to a thorough cooling of the lower air strata, and presumably a marked inverted temperature gradient, the audibility was excellent, the sound being refracted downward, and all objects "looming," as it were. It is even possible to work out the retardation or acceleration of the wave front with the degree of variation in temperature. Finally, it may be that the temperature and the air motion may act together to refract downward the sound wave, and it may also happen that the one influence may oppose the other. Thus Reynolds gives an example where, with a heavy dew on the ground, sound could be heard equally well against a light wind as with the wind

"Showing that the upward refraction by the wind was completely counteracted by the downward refraction from the diminution of temperature. This was observed not to be the case when cloudiness at night prevented terrestrial radiation." (Proc. R. S., 1874.)

The presence of large quantities of condensed water vapor brings us to the question of refracting surfaces and the reverberation of the sound rather than its velocity.

When a sound wave travels over a perfectly smooth surface, such as a glassy sea, or a sharply outlined plane of condensation, the intensity of the sound does not diminish with the usual rapidity. In discussing the propagation of sound in whispering galleries, Rayleigh" shows that the abnormal loudness is not confined to a point diametrically opposite that occupied by the speaker, but that there is a bending or clinging of the sound waves to the surface of the concave wall. Sonorous vibrations at fog surfaces and cloud surfaces may behave in a somewhat similar way, and it is probable that the curvature of the surface is not of as great importance as the comparative smoothness of the surface. Probably the roll of thunder is an excellent illustration of continued reverberation at cloud surfaces.

WRECK OF THE PACIFIC MAIL STEAMSHIP RIO DE JANEIRO."

Any memoir upon the fog of San Francisco Bay would be incomplete without a reference to one of the most remarkable of marine accidents. On the morning of Friday, February 22, 1901, the Pacific Mail steamship Rio de Janeiro ran upon the Fort Point Reef during a fog. Within fifteen or twenty minutes from the time of striking the vessel sank, and of the 210 persons on board 130 were lost. Another statement, purporting to be official, makes the total number aboard 207 and the lost 127.

The following facts are obtained chiefly from the statements of Pilot F. W. Jordan. The ship's master, Capt. William Ward, went down with the vessel. The pilot boarded the Rio de Janeiro in the vicinity of the 9-fathom buoy, near the bar buoy, and anchored in 13 fathoms at a little before 6 o'clock Thursday night, February 21. The weather being foggy, the ship remained at anchor till about 4 a. m., one hundred and twentieth meridian time, when the fog lifted and the Cliff House light could be seen, but not the Point Bonita light. Preparations were in progress to steam into the harbor, when a dense fog came out from the Golden Gate, obscuring everything. There is some difference of testimony as to whether the captain or the pilot gave the orders to proceed in the fog, but the vessel was started on a northeast course with Lime Point straight ahead, steering by the whistle. The pilot expected to get an echo of the ship's whistle from Point Diablo, but heard none. The course was changed north-northeast with the intention of running close to Lime Point. The vessel was not moving at full speed and was subject to a strong cross current, which, apparently acting at right angles to the length of the vessel, carried the ship to the south, far out of the proper course. The first officer was standing on the starboard side listening for the Fort Point bell. No soundings, however, were taken. The vessel struck a short distance to the southwest of the Fort Point light. At the moment of striking the pilot saw the white flash at Fort Point and heard the Fort Point bell.

The pilot had had eleven years' experience in the harbor and was considered one of the most capable pilots in San Francisco. He had never previously met with an accident. There appears to be no doubt of the existence of the strong cross current, inasmuch as other vessels entering

a Theory of Sound, vol. 2, sec. 287.

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