GEODETIC SURVEYING INSTRUMENTS AND METHODS OF OBSERVATION In a sketch of this sort it would not be desirable to enter into details about the design, construction and use of the instruments 'It may seem as if just the reverse would be true, but this is be cause the reader may be thinking of the length of a degree of geocen tric latitude, that is the length of an elliptical arc subtending an angle of one degree at the center of the Earth. The latitude meant, however, is not the geocentric latitude, which is not susceptible of direct observation, but the astronomic latitude (see LATITUDE), which is the angle between the plumb-line and the plane of the equator. The plumb-line is assumed to be normal to the meridian section through the place of observation. The ratio of the change in latitude to the change in linear distance from the equator is obviously a measure of the curvature, and the curvature of an ellipse (which may be taken as typical of all symmetrical ovals) is obviously greatest at the vertex, which corresponds to the end of the major axis or to the equator, and least at the end of the minor axis, that is, at the poles.
then Spanish province of Peru included what is now Ecuador, where all the geodetic work was done. The word "Peru" has become inseparably attached to this expedition. The measuring bar used was called the "toise of Peru" and because it was made with special care it became the standard of length on which much later geodetic work was based. A toise consisted of six French feet, equivalent to a little less than 6 feet 5 inches English measure.
was intended that the meter should be one ten-millionth of the length of the quadrant of a meridian, as nearly as could be deter mined. With the meter established, however, as a length defined by a certain standard bar, this bar serves as the definition, and later determinations of the figure of the Earth have no effect on the length of the meter.
employed in geodesy. The instruments used in the astronomical part of the work for determining latitude and longitude are simply the ordinary astronomical instruments for those purposes. For longitudes the transit instrument is, and has been for a long time, in general use. Nowadays it is ordinarily provided with a self recording micrometer and is used in connection with a chrono graph. For latitude determinations the zenith telescope and the broken-telescope transit are in almost universal use. For the determination of azimuths and for the measurement of the angles of triangulation, theodolites are used, of a type more accurate than those needed in ordinary surveying but not differing from them in principle. As an additional means to secure greater accuracy a large number of measurements are taken, the pointings on any given object being evenly distributed around the horizontal circle of the instrument, in order to eliminate errors of graduation as far as possible.
The sides of the triangles are of any convenient length up to the maximum length of intervisibility between stations. Excep tionally this may be 200 miles or more in mountainous regions, and too miles is by no means unusual. At the other extreme, it is not desirable to make the sides of the principal triangles too short, for then errors in centering both the instrument and the object sighted on play too large a part. Moreover, too many trian gles, each subject to error, are then required for a given amount of linear progress. The practical lower limit for the best work is now considered to be about 2 miles. Theoretically, one measured base connected with the triangulation and taken in conjunction with the measured angles would suffice to determine the lengths of all the sides of the triangles, but in practice directly measured bases are connected with the triangulation at frequent intervals. The accuracy of a base directly measured is much greater than that of the length of the same line computed by means of angular meas urements from another measured base, though the two bases may be separated by only a few intervening triangles. The direct measurement of frequent bases serves therefore as a check on the measurements of angle.
Formerly bases were measured with bars or rods. Great care was necessary in making contacts between the ends of the bars and in determining their temperature, which might not be the same as the temperature of the surrounding air, because the expan sion of the bars by heat made a very appreciable difference in their lengths. Nowadays bases are measured with tapes or wires made of invar alloy. The coefficient of the thermal expansion of this alloy is so low that the temperatures need not be determined with any great accuracy. The wires or tapes are always used at a standard tension maintained with weights and pulleys, or with spring balances, and their lengths are accurately determined in a standardizing laboratory—under conditions similar to those in the field—both before and after a campaign in the field. In this way the accuracy of a base measured with invar tapes or wires is quite as great in practice as that obtainable with the more elaborate and cumbrous base-bar apparatus used during the 19th century. Roughly speaking, an accuracy of one part in soo,000 or even one part in i,000,000 may be obtained in base measure ments.
The instruments for precise leveling are in principle the same as the usual engineering instruments for spirit leveling, but various refinements have been introduced into the design, and special precautions to secure accuracy are adopted.
The gradual increase in the accuracy of geodetic observations has been accompanied by an increasing precision in definition of the quantities sought and an increasing attention to details of theory. When we say that we are endeavouring to determine the figure of the Earth, we are not concerned with the exact contours of the hills, valleys and ocean basins. These are matters for the topographer and hydrographer. The forms of these superficial features are specified with reference to a surface that defines the figure of the Earth. Over the sea this surface is mean sea level, and beneath the land it is an imaginary sea-level surface defined by spirit leveling. If small sea-level canals were dug into the interior of the continents or open-ended pipes like inverted siphons were run from the land out into the ocean, the surface sought would be defined physically at various points by the level of the water in these canals or pipes. But even this physical definition lacks mathematical precision. Sea level is affected by winds, salinity, barometric pressure and temperature. What is really sought is the form of what is known mathematically as an equi potential surface or level surface, characterized by the fact that over its entire extent the so-called potential function is constant. This potential function is due to the effect of the gravitational attraction of the matter composing the Earth, as it is and where it is, combined with the effect due to the rotation of the earth about its axis. Any shifting of mass such as would be implied in the digging of the supposed sea-level canals would change slightly the form of these equipotential surfaces; and so, to be accurate, we must resort to the mathematical fiction that these canals are to be infinitesimal.
There is an indefinite number of equipotential surfaces all characterized by the property that they are everywhere perpen dicular to the direction of the apparent gravity'. What is sought is the form of the particular equipotential surface that most nearly coincides with the mean level of the ocean. The figure of this surface is by definition the figure of the Earth, and the surface is termed the Geoid, a term invented to avoid any commitment in advance of exact knowledge as to the exact shape of the Earth, for the use of this non-committal term merely means that the Earth is Earth-shaped. We know of course that it is approxi mately an ellipsoid of revolution flattened at the poles. Spirit leveling gives the elevation of points with respect to the geoid', not with respect to the terrestrial ellipsoid.
For mapping purposes it is customary to use an ellipsoid of revolution as an adequate and convenient substitute for the geoid. The dimensions and orientation of the assumed ellipsoid may represent an attempt to find the ellipsoid that most nearly fits the geoid as a whole, or they may represent an attempt to fit only a particular part of the geoid without regard to the rest of it. When we speak of the figure of the Earth we usually mean the dimen sions of the ellipsoid most nearly representing the geoid as a whole. If the Earth is assumed to be a sphere, the length of a single meridional arc with the difference of latitude of its end points suffices to determine its size. If it is assumed to be an ellipsoid of revolution, at least two meridional arcs and the lati tudes of all end points must be determined. If we have more than two such arcs, various combinations of them two and two will not give precisely the same result because the geoid is not exactly an ellipsoid. The accepted way down to the middle of the 19th century was to take as many meridional arcs as might be available, rejecting perhaps those whose end latitudes were judged abnormal because of marked topographical relief in the vicinity, and recon cile them as well as might be by some arbitrary procedure or later by a least-squares adjustment.
It is obvious that if differences of longitude could be obtained as accurately as differences of latitude, measured arcs of parallel would serve as well as measured meridional arcs to determine the figure of the Earth. There were methods of determining astronomi cal differences of longitude before the invention of the electric telegraph, and arcs of parallel were measured, but little weight was given to them because of the inaccuracy of the astronomic longi tudes. With the invention of the electric telegraph' differences of longitude began to be used, at first in much the same way as differ 'Gravity, as here used, means the combined effect of gravitational attraction and the centrifugal force of rotation.
'Except of course in so far as the relation of the geoid to the assumed mean sea level on which the leveling operations are based may be uncertain for reasons already given. Strictly speaking, a knowledge of gravity at points along the level line is also needed, but this is a refinement that need not be here considered.
radiotelegraphy has been used with great success in the determination of longitudes. By this method it is easier to determine the longitude of a large number of points than when the electric telegraph is used, and it is possible to select, if desired, points remote from towns. There is no difference in principle, geodetically speaking, between the two methods but only differences in technical detail.
ences of latitude, but later in connection with what may be called the area method or the deflection method of determining the figure of the geoid'', in contradistinction to the arc method, or method involving only unconnected arcs of meridians and parallels.
The area or deflection method supposes a considerable extent of territory more or less covered by connected chains of triangula tion. Somewhere in the midst of this triangulation a point is taken as the origin, a latitude and a longitude are assigned to this point, an azimuth is also assigned to a side of one of the triangles passing through this point. The latitude, longitude and azimuth are to a certain extent arbitrary, but it would not be usual or con venient to assign to them values differing greatly from the astronomic values of those quantities. Besides these, dimensions of the terrestrial ellipsoid are assumed. These five quantities, the latitude and longitude of the initial point, the azimuth of a line through the point, and the two parameters necessary to specify the dimensions of the terrestrial ellipsoid of revolution, constitute a geodetic datum for the area covered by the triangulation. For instance, for the triangulation of the United States the initial point is Meades Ranch in Kansas, latitude 39° 13' 26".686 longitude 98° 32' 30"•506, azimuth to Waldo 75° 28' 14"•52. The dimensions of the terrestrial spheroid used in computing the triangulation are those known as the Clarke Spheroid of 1866 expressed in meters, namely semi-major axis 6,378,206.4 meters and semi minor axis 6,356,583.8 meters.
The triangles are assumed to lie on the assumed ellipsoid and from the assumed values for the origin and the known sides and angles of the triangulation the latitude and longitude of every vertex of every triangle and the azimuth of every side may be computed, all without reference to the astronomic values of those quantities. The quantities so computed are termed the geodetic latitude, west longitude and azimuth. If we denote these quantities by 4, X and a, affecting them with subscript A or G to denote re spectively the astronomic or geodetic values, the deflections or differences between the astronomic and geodetic verticals are : Stations at which observations of both longitude and azimuth are available are called Laplace stations ; at such stations there are two determinations of the deflection in the prime vertical. These should be made consistent ; in doing this the geodetic azimuth generally receives most of the correction, as it is much more sub ject to an accumulation of error than the geodetic longitude.
The deflections obtained in this way obviously depend on the geodetic datum used. It is usual to assume, in accordance with the principle of least squares, that the best geodetic datum is that which makes the sum of the squares of the deflections (weighted, perhaps, according to some principle) a minimum. The dimensions of the ellipsoid constituting part of this geodetic datum then represent the figure of the Earth for this territory.
It should be noted that geodetic latitudes, longitudes and azimuths, as previously defined, are quantities dependent partly on convention, that is, on the assumed geodetic datum, and partly on a series of observed quantities, that is, the angles and sides of the triangles; a least-squares adjustment may also be involved. The geodetic latitude, longitude and azimuth at a station are then not capable of immediate verification by direct observation on the spot as the corresponding astronomic quantities are, except of course that the longitude must be referred to the prime meridian.
The difference between an astronomic latitude, longitude or azimuth and the corresponding geodetic quantity is usually small. The average value is only a few seconds of arc and differences of over 1o" of arc are rare except in mountainous regions. There is, however, a classic instance of large deflections of contrary sign at stations no great distance apart in the midst of a plain near Moscow. Some mass of abnormally low density must lie beneath word geoid is used advisedly rather than Earth, because it may be the purpose to determine by the deflection method the figure of a portion of the geoid in the given area rather than to determine the figure of the Earth as a whole.
the surface. It might seem as if the astronomic values of the lati tude and longitude would be the ones used for mapping purposes; but this is not the case. Where the geodetic values are available they are invariably used in preference to the astronomic values, in spite of the conventional and derivative character of the former. This is because astronomic latitude and longitude depend on the direction of the plumb line and are therefore so affected by local topographic conditions as to render inaccurate any de terminations of distance and direction based on the astronomic values.
For instance, if we used the astronomic latitudes of two points one on the north coast of Porto Rico and one on the south coast, and computed the distance between them from these latitudes and from the known size of the Earth, the distance would come out about a mile in error, or about one part in 5o, as against an ac curacy of one part in i oo,000, or better, obtainable from direct measurement by triangulation. Again, the western part of the boundary between the United States and Canada is the 49th parallel of latitude ; for reasons of convenience this parallel was defined astronomically, and the result is that in one instance one bounding station is about 8" north of where a geodetic determi nation would have put it, and another station less than ioo miles away is some 6" south. The greatest relative error between two adjacent stations is about 7" in a distance of 20 miles, which would mean an error in the direction from one station to the other, as inferred from the latitudes, of about 35 ft. to the mile.
These irregular deflections of the plumb line have plagued geodesists from the beginning ; they far exceed the errors in either the astronomical or geodetic determinations, and even for a comparatively small region they cannot be greatly reduced by changing the geodetic datum. If the region covered is large or if the same dimensions of the terrestrial ellipsoid are used for several separate regions, the deflections are still larger.
At first the only feasible procedure for determining the figure of the Earth as a whole was to reject those arcs where the ruggedness of the topography seemed likely to introduce ab normally large deflections, treat the remaining deflections like accidental errors, and hope that their effects would more or less balance out in the final result. As better topographic maps be came available and geodetic surveys became better organized, it began to seem feasible to calculate by some sort of mechanical integration the effects of the visible topography—mountains, plateaus, valleys, ocean basins, etc.—on the direction of the plumb line, that is, on the deflections. J. H. Pratt, archdeacon of Calcutta, was the first one to try calculations of this sort on a large scale with some attempt to make the calculations apply with fair approximation, even at the expense of considerable labour, to the actual topography instead of to highly convention alized geometrical substitutes for it.
Pratt found, what had already been suspected, that although the plumb line was in general deflected toward a hill, a range of mountains, or the interior of a continent, and away from a hollow, a valley, or the ocean deeps, nevertheless the amount of such deflection was in general considerably less than the amount com puted by taking these topographic features at what might be termed their full face value. The most satisfactory way of obtaining approximate agreement between the observed and the computed deflections was found to be the assumption that ap parent excesses of matter protruding above the geoid, such as hills, mountain ranges and continents, and apparent deficiencies of matter where the Earth's surface is depressed below the level of the surrounding country, or indeed below the level of the geoid, such as valleys and ocean basins, are not real excesses or deficiencies of matter, but that these apparent excesses or de ficiencies are compensated. That is, beneath each apparent excess as represented by the surface form there is somewhere a de ficiency of density, so that there is little or no real excess of matter ; similarly, below each apparent deficiency of matter as revealed by surface configuration there is a compensating excess of density. In short, under mountain ranges and plateaus the density of the crust is less and under the oceans greater.
It is convenient for mathematical reasons and is in fair agree ment with the observed facts to assume that the excess or de ficiency of mass, as shown by surface conformation, is exactly com pensated by the subterranean deficiency or excess of density. This compensation is called isostatic compensation and the correspond ing state of affairs isostasy, a name invented by C. E. Dutton. To state the matter differently: assume unit areas at some depth to be specified later and called the depth of compensation in different regions, and compare the total mass standing upon the various unit areas. The hypothesis of isostasy states that the amount of matter standing upon a unit area will be the same re gardless of whether it is under highlands or lowlands, continents or ocean deeps. It is not to be supposed that the unit area may be taken indefinitely small, or that the state of isostasy is perfect. A circle with a radius of ioo miles is almost certainly large enough to serve as a unit area, and a much smaller circle might be large enough in most cases.
There are two competing hypotheses as to the way in which isostatic compensation is effected; to these the names of Pratt and of Sir George Biddell Airy, former Astronomer Royal, have been attached. According to the Pratt hypothesis there is a definite depth of compensation, the crustal material underneath the higher parts of the surface being less dense and under lower parts more dense, so that the total mass standing on any unit area is the same. The Airy theory is, roughly speaking, a flotation theory, the blocks of lighter crust floating in a denser plastic material, which Airy called the lava, but which modern geologists prefer to call magma'. The deficiency of density corresponding to a height of land is secured, not in the upper part of the crust, but in the "root" which projects down into the denser magma and displaces it. Just as a tall iceberg means one that extends far below the surface, so a high mountain or plateau has its roots dipping deep into the magma. On the Pratt hypothesis the depth of compensation is perhaps 6o miles (Ioo km.), according to investigations of Bowie and others, but this is merely an average figure. On the Airy hypothesis the lighter crust extends down to an average depth of perhaps half this, say 3o miles or less; less under the oceans, more under the continents and highlands. As a rule geologists prefer the Airy hypothesis, as more in accordance with their way of thinking, but most of the existing computations have been made according to the Pratt hypothesis. For geodetic purposes there is not much to choose between the two hypotheses.
When the deflections are applied to determine the ellipsoid that best fits a comparatively small region, the deflections that are to be minimized by the method of least squares should be the actual deflections for which formulas have previously been given. But if it is desired to make the region to which the deflections apply representative of the earth as a whole in order to determine the figure of the earth, then the deflections should be corrected for the visible surface topography and its presumed isostatic com pensation.
This isostatic method was first applied by Hayford to observa tions extending over the United States. In spite of the limited extent of the territory covered—in comparison with the land sur face of the globe—the figure of the Earth deduced by him was adopted in 1924 by the Section of Geodesy of the International Geodetic and Geophysical Union as the best available figure of the Earth as a whole. This terrestrial ellipsoid thus determined is known as the International Ellipsoid of Reference. Heiskanen applied the isostatic method to deflections of the vertical in Europe and found results agreeing substantially with Hayford's. The dimensions of the International Ellipsoid are given in a later section. The conclusions regarding isostasy derived from a study of the vertical are in general supported by a study of the observations of gravity discussed in the next section.
centric spherical shells, its attraction would be uniform all over its surface and would be directed towards the common centre. For the sake of simplicity, let us imagine that the Earth had this spherical form at the start and then acquired its present rotation about its axis. Even if the Earth were absolutely rigid and un yielding the "centrifugal" force of rotation, being zero at the poles and a maximum at the equator, would introduce a variation into the apparent gravity, a variation dependent on the latitude. The substance of which the Earth is composed is, however, not unyielding, but gives way under the "centrifugal force" so that the Earth has approximately the form that it would have if it were fluid and in equilibrium under the combined forces of its own attraction and the "centrifugal force" of rotation ;' its form is nearly that of an ellipsoid of revolution flattened at the poles. This departure from the spherical form is a further cause of a change of apparent gravity between poles and equator.
The intensity of gravity can be measured very accurately by means of the oscillations of a pendulum' and from the variation in gravity between equator and pole the flattening or ellipticity of the earth may be determined.
The process is as follows : From theoretical considerations it is known that the gravity on the surface of an ellipsoid of revolution, this surface being at the same time an equipotential surface, may be written in the form go = gE(I + b sine 4)— sine 24).
Here is gravity at the surface in geographic latitude 95, is gravity at the equator, b and are constant coefficients, depend ing on the flattening. The coefficient is small and the flattening is sufficiently well known so that its value may be set down in advance as o.000006 for an exact ellipsoid. This leaves two co efficients, and b, to be determined by observation. Theoret ically, two values of g in different latitudes would suffice for this. In practice as many gravity stations as are available are used, the discordances being adjusted by the method of least squares. These discordances arise from the fact that the earth is not an exact ellipsoid of revolution, as is assumed in the formula, and furthermore that local topographic and geological conditions, that is, the existence of mountains, valleys, oceans, and abnormally high or low densities in the neighbourhood of a gravity station, cause deviations from any theoretical formula that can be de vised. These deviations are called gravity anomalies.
When the best obtainable values of the coefficients and b have been found the flattening f is found from the relation b= 5 _ r 7 wza — f r4 2 gE Here a is the equatorial radius of the ellipsoid, which must be known in advance and w is the angular velocity of the Earth's rotation. This formula is due in substance to Clairaut (q.v.), who, however, did not push his approximations far enough to include the term This term is correct only when, as stated, the 14 Earth's surface is assumed to be exactly that of an ellipsoid of revolution.
The observations of gravity are generally taken at or near the surface of the Earth, though occasional observations have been made in mines. The formulas given refer to the ideal level sur face of the spheroid or ellipsoid. The observed values of gravity 'Mountains, plateaus and ocean deeps are obvious exceptions ; they are supported by the stiffness of the outer crust, but the general conformation of the Earth is as stated. On the subject of fluid equilibrium see in this article under the subhead Isostasy.
the same pendulum is swung at two different places and the periods of an oscillation there are found to be tl and t2, the values of gravity gi and g2 at the two places are connected by the relation The modern process of determining the figure of the earth from gravity observations depends on this formula for the relative gravity at two places. Relative gravity may be determined within one or two parts in a million. The absolute value of the acceleration of gravity at any given place is found from the formula l being the length of the pendulum. The accurate deter mination of absolute gravity is much more difficult, on account of the complications arising in measuring 1.
could be reduced to this level surface by adding where H is the height of the point of observation above the level surface in question.' But we do not know our elevations with respect to the ellipsoid or spheroid of reference. The best avail able approximation is the elevation with respect to the geoid. Observations of gravity are then reduced to the geoid, which is treated as if it were a regular surface. The coefficients and b are found by a least squares adjustment, b4 being so small that a very approximate value of the flattening determines it with more than sufficient accuracy, and from these the value of the flattening f is obtained. Theoretically it is possible to determine a also, but the determination is so poor as to be valueless. Gravity observa tions thus determine the shape but not the size of the terrestrial ellipsoid.
The preceding formula for the correction for the elevation of the station is derived on the supposition that there is no matter intervening between the station and the level surface to which the observation is reduced, a method based on a supposition mani festly false and yet found to work better on the whole in prac tice than the method of computing the effect of all visible surface irregularities either in the neighbourhood of the station only or over the entire globe and taking this effect at its full face value. This fact is another manifestation of isostasy. The effect of the visible irregularities of the surface is largely counteracted by effects of contrary nature in the crust beneath them. This was noticed very early. In the expedition of the Paris Academy to Peru Bouguer swung his crude pendulums at sea-level and then at Quito in about the same latitude but over 9,00o feet above sea level. He found to his surprise that the land masses below the level of Quito seemed to have much less effect than they appar ently should. Later writers commented on this and speculated on the possibility of extensive cavities, but it was not until over a century later that Pratt undertook the extensive computations that established isostasy on a comparatively secure basis.
Gravity observations may be used not only, as has been stated, to determine the flattening of the terrestrial ellipsoid but also to determine the deviations of the geoid from this assumed ellipsoid. The practical possibility of this was shown by Sir George Gabriel Stokes (q.v.) in 1849, but the requisite observations seemed then unobtainable, for Stokes' theory required that gravity be observed at fairly close intervals over the entire globe, including the sea, and there seemed no way to do this with the requisite accuracy.' Various devices were tried for measuring gravity at sea, the most successful, until very recently, being a method due to Hecker based on the comparison of the atmospheric pressure obtained by a determination of the boiling point of water with that obtained by a direct reading of the mercury barometer. Hecker's method was accurate enough to prove that in a general way isostasy prevailed over the oceans as well as over the land, but the accuracy obtained by great labour and complication was far inferior to that easily obtainable on land with the pendulum.
Finally, a Dutch geodesist, Vening Meinesz, in seeking to overcome the difficulties of the unstable support of the pendulum apparatus in a country like Holland where the land itself is none too stable, hit on the idea of eliminating the horizontal accelera tion of the pendulum, which was found to be the principal cause of the difficulty, by swinging two pendulums in the same vertical plane and therefore subject to the same horizontal acceleration. By using a certain hypothetical pendulum, the phase of which at any instant is the difference between the phases of the two pendulums at that instant, the effect of the horizontal acceleration was eliminated. The idea was found capable of adaptation to even more trying conditions than those presented by the unstable soil of Holland. By using an improved form of the apparatus in a submarine vessel submerged deep enough to escape most of the motion on the surface of the sea, and by supporting the apparatus 'The factor of H is nearly constant and corresponds to a variation in gravity of about one part in r,000,000 for each three meters (or ro ft.) of elevation.
on gimbals, it was found possible to get gravity observations on the open ocean. The accuracy obtainable is not quite as great as on solid land but the results are nevertheless very gratifying.
In this way Meinesz has observed gravity at 25o ocean stations mostly in low or middle latitudes. It is to be hoped that, soon, enough ocean gravity stations will be observed over all oceanic areas so that when taken in conjunction with the numerous sta tions on land they will enable the bumps and hollows of the geoid to be determined by Stokes' method, that is, bumps and hollows when compared with the regular mathematical surface of the terrestrial ellipsoid.
Enough has already been learned to raise interesting questions. In regard to the perfectness of the isostatic condition over ocean areas there seem to be two opposite tendencies toward imperfec- ' tion. On the one hand, stations over great ocean deeps show a tendency toward abnormally small gravity—from the point of view of perfect isostasy—as if the hollows in the sea bottom rep resented real uncompensated, or only partly compensated, deficits of matter. On the other hand, there seems to be a slight though definite tendency toward an excess of gravity—still from the point of view of perfect isostasy—over ocean areas in general. Some indication of this state of affairs had previously been given by gravity observations on land. The theory of isostasy would predict slight hollows in the geoid over oceanic areas. The fact seems to be that there are slight bumps. It is well, however, to be cautious in drawing conclusions as the observational evidence is still rather meager and no consensus of opinion has been reached in regard to the interpretation of it.