He considered that down to the beginning of this century astronomical instruments had not been able to show any variation of latitudes. There were differences, but these he thought could be accounted for as errors of observation.*

To-day, however, we feel certain that small variations in latitude are taking place, but so small that practically, in map making, for example, and in navigation, they are of no importance, though scientifically very important.

It might also, in this connection, be stated that there are theoretical reasons which seem to indicate that the earth's rotation time is not only changing, but also is not altogether uniform. The effect of the tidewave as it moves west over the earth is to act as a friction-brake on the revolving earth, and so slow up the rotation time, and as this tide effect is not always the same the retarding effects differ, and theoretically produce a non-uniformity in the rotation time. But the shrinkage of the earth, due to loss of heat, would tend to make it revolve more rapidly. These effects may work against each other. However, observations and calculations to-day do not furnish us with any certain evidence that the rotation time is longer or shorter than it was ten centuries ago.

It no doubt will happen that, when observations and instruments are much improved, astronomers will discover these slight changes in rotation time that theory seems to require.

The idea that the latitudes of places change is not a new one.

Down to about the time that the telescope was invented there were many learned persons who believed that the latitudes of

*The writer is much indebted to the paper by Professor Doolittle on 'Variations of Latitude' read before the A. A. A. S., at Madison, Wis., August, 1893.

of centuries. These ideas were based on a comparison of maps made at different times.

A disciple of the illustrious Copernicus considered that the evidence was conclusive, and was satisfied that the pole of the earth was changing its position in a progressive manner; he considered that in time the torrid and frigid zones would change places.

However, these views of Dominique Maria de Ferrare were founded on poor data. The latitudes of a few places had been determined, by very imperfect means, in the best way they had, viz., from the shadow cast by a gnomon; but the latitudes of many places on the maps were put in from the accounts of travelers, the time it took to travel from one point to another being used as the basis of calculation.

Even in these enlightened days, as we like to consider them, there is no good map of our own Empire State. The latitudes of a few points only in New York State have been determined with accuracy. But there are many places in the State whose positions are not known within more than a mile.

In the latter part of the 16th century Tycho Brahe, of Denmark, improved the instruments in use (without the telescope), and later, about 1610, the telescope was discovered and applied to astronomical instruments. Then new and more accurate methods were used to determine latitude, and the large discrepancies disappeared. Some observers found differences between latitudes determined in winter and in summer, and they supposed those differences to be due to changes of the pole.

In the latter part of the 17th century J. D. Cassini summed up the state of the problem in his day, and arrived at the conclusion that, notwithstanding the apparent variations in the latitudes, the pole of the

earth did not change to any large extent; that most of the apparent changes in latitude were due to errors of observation and defects in theory, but he thought it probable that small changes did occur in the position of the pole; he thought the changes were periodic, and did not amount to more than two minutes of arc equal to about 12,000 feet.

"Thus, instead of several degrees which were conceded by the astronomers of of previous centuries, but a paltry two minutes was now allowed; but with improved instruments, with the discovery of aberration and nutation and the perfection of the theory of refraction, even this modest allowance was gradually reduced to a vanishing quantity."

The geologists, in their investigations, have found fossil remains in the cold regions of the north, belonging to the Miocene, Upper and lower Cretaceous, Jurassic and other geological periods, which seem to indicate a former temperature much higher than the present. In 1876 Dr. John Evans, then President of the British Geological Society, discussed the problem, and concluded that the amount of polar light and heat in the past must have been much greater than it is now. He invited the attention of the mathematicians to this problem, and asked: Would a considerable elevation and depression of the sea bottoms and continents produce a 'change of 15 degrees to 20 degrees in the position of the pole?'

Sir William Thomson discussed this problem and gave his conclusions in 1876 to the British Association for Advancement of Science. He said: "Consider the great facts of the Himalayas and Andes and Africa, and the depths of the Atlantic, and America and the depths of the Pacific, and Australia; and consider further the ellipticity of the equatorial section of the sea level, estimated by Colonel Clarke at about one-tenth of the mean ellipticity of the meridianal sections of the sea level.

"We need no brush from a comet's tail to account for a change in the earth's axis; we need no violent convulsions producing a sudden distortion on a great scale, with change of axis of maximum moment of inertia, followed by gigantic deluges; and we may not merely admit, but assert as highly probable, that the axis of maximum inertia and the axis of rotation, always near one another, may have been in ancient times very far from their present geographical position, and may have gradually shifted through ten, twenty, thirty or forty or more degrees without at any time any perceptible sudden disturbance of either land or water."

Sir William Thomson gave no account of the calculations made by him as the basis of these conclusions.

In 1877 Mr. G. H. Darwin made a careful and elaborate mathematical discussion of the problem. He showed that, in a perfectly rigid globe, the pole could not have wandered more than 3 degrees from its original position, as the result of the continents and oceans changing places. "If, however, the earth is sufficiently plastic to admit of readjustment to new forms of equilibrium, by earthquakes and otherwise, possible changes of ten or fifteen degrees may have occurred. This would require, however, such a complete changing about of the continents and oceans, with maximum elevations and depressions in precisely the most favorable places, as has certainly never occurred in geologic times."

The evidence indicates, in fact, that the continental areas have always occupied about the same positions as now.

Thus it would seem that the geologists must abandon the hypothesis of great changes in latitude as a factor in the earth's development, unless a new cause can be found that will move the pole to the extent required by the geologists.

In an address made before Section A, of the British Association in 1892, Professor

Shuster stated that he believed the evidence at hand was in favor of the view that there was sufficient matter in interplanetary space to make it a conductor of electricity. This conductivity, however, must be small, for if it were not, he said, the earth would gradually set itself to revolve about its magnetic poles. However, changes in the position of the magnetic poles would tend to prevent this result. Perhaps the investigator in the near future, working on the suggestion of Dr. Shuster, may find some connection between the earth's magnetism, rotation time and position of rotation axis.

The evidence, then, at this phase of the discussion, is in favor of the view that there is no adequate reason for believing that any large changes of latitude, amounting to several degrees, have occurred in geologic times. The evidence shows, however, that there are small changes. Are they progressive; does the north pole of the earth wander slowly but surely further and further away from its positions of ages gone by?

At the International Geodetic Congress held in 1883 at Rome, Sig. Fergola, of the Royal Observatory Cappodimonti, Naples, gave a tabular statement which seemed to show that small but progressive changes had taken place in Europe and America. This table showed, for example, that the latitude of Washington, D. C., had decreased from 1845 to 1865, 0.47"; at Paris, from 1825 to 1853, the decrease was 1.8"; at Milan in 60 years, 1.5"; at Rome during 56 years, 0.17"; at Naples in 51 years, 0.22"; at Königsberg in 23 years, 0.15"; at Greenwich in 19 years, 0.51". Fergola, at the Congress mentioned, suggested a plan for making systematic observations, and he pointed out the favorable location of several observatories that were on nearly the same circle of latitude, but differing widely in longitude. Unfortunately this suggestion of Fergola's was not carried out in any way until 1892, when the Columbia College Observatory arranged

to work in conjunction with the Naples Observatory on the problem. This series of observations was begun in the spring of 1893, and will be continued several years.

The data given by Fergola at Rome in 1883 showed a diminution of latitude in every case; other data showed a similar diminution; however there were exceptions, where the latitudes seemed to in

crease.

The investigations that have been going on since 1883 throw doubt on the progressive changes in latitude, or at least such changes are masked by proved periodic changes.

For a long time, since 1765, periodic changes have been looked for, because the theory of a rotating earth, an earth having the form of a sphere flattened at the poles, or, more accurately, an ellipsoid of revolution, demanded such changes; but the theory did not furnish any clue to the amount of changes, except that they must be very small. This theory shows that if the earth was absolutely rigid and revolved about its shortest axis (called the axis of figure) at any time it would continue to revolve about such axis forever, unless disturbed by some outside force. If so disturbed, then the axis of rotation would no longer coincide with the axis of figure-the axis of rotation would intersect the earth's surface at points away from the points where the axis of figure comes out. But the theory also showed that the new axis of rotation would revolve about the old one in a period of 304.8 days. This period comes from the knowledge of the magnitude of precession and nutation, and is known very accurately.

We would expect therefore that changes in latitude would show this 305-day period.

Several attempts have been made to determine the distance between the two axes (figure and rotation axis) from changes in latitudes.

The celebrated astronomer Bessel made

the first attempt, and was unsuccessful, it was supposed until recently.*

Observations were also made at Pulkova, Russia, Greenwich and Washington. The Washington observations were made between 1862 and '67, and included six complete periods of 305 days each. A rigorous discussion by Newcomb gave the separation of the axes as 3 feet, or 0.03".

to determine the separation of the axis of rotation and axis of figure, were going on that Sir Wm. Thomson (now Lord Kelvin) announced, at the Congress of the British Association at Glasgow in 1874, that the meteorological phenomena, the fall of rain and snow, the changes which occur in the circulation of the air and of the sea waters would modify a little the mechanical con

These figures are small, but fairly accordant. A reinvestigation, however, showed that the various calculations did not agree in showing the same displacement at the same time. This made the whole result doubtful, so that Newcomb (in 1892, March, Mon. Not. R. A. S.) remarked that "the observations showed beyond doubt there could be no inequality of the kind looked for."

*Tisserand says in Ann. Bur. Long. '95 (P. 42, B. 11) that there is a letter of April 7, 1846, in which Humboldt replies to Gauss that Bessel had told him in 1844 that his observations showed that his latitude had decreased 0. 3' in two years. Bessel attributed this variation to changes accomplished in the interior of the globe. See also Hagan's letter in Astr. Nach., September, 1894.

In this connection it ought to be noted also that Prof. J. C. Maxwell read a paper April 20, 1857, before the Royal Society of Edinburgh (see Transactions Roy. Soc. Edinburgh, Vol. XXI., Part iv., pp. 559–571), ‘On a Dynamical Top for exhibiting the phenomena of the motion of a system of invariable form about a fixed point, with some suggestions as to the earth's motion.' He deduced a period of 325.6 solar days. He examined the observations of Polaris made with the Greenwich Transit Circle in the years 1851-54. He found the apparent co-latitude of Greenwich for each month of the four years specified.

"There appeared a very slight indication of a maximum belonging to the set of months, March, '51; February, '52; December, '52; November, '53; September, '54." This result, he says, "is to be regarded as very doubtful, as there did not appear to be evidence for any variation exceeding half a second of space and more observations would be required to establish the existence of so small a variation at all."

make scientific men give the statement great attention. These meteorologic phenomena of which Sir William Thomson spoke are annual in character. When this annual period is combined with the 305day or ten-month period of Euler we see that complexity results. This was the state of the investigation when Dr. Küstner, of the Berlin Observatory, published the results of his observations made in 18841885. Dr. Küstner undertook some observations for the trial of a new method for the determination of the constant of aberration. On reducing his observations he obtained results which were not at all satisfactory. A careful examination of his work led him to make the announcement that the unsatisfactory value for the aberration constant was due to a comparatively rapid, though very small, change in the latitude of the Berlin Observatory-"that from August to November, 1884, the latitude of Berlin had been from ".2 to ".3 greater than from March to May in 1884 and 1885."