The seas surrounding Sweden are particularly well adapted for 

 the study of periodicities in the oceanic circulation and its depen- 

 dance on the tide-generating force. The tidal movement, almost 

 imperceptible at the surface, reappears on a A^astly enlarged scale 

 as great submarine waves in the borderlayer between the surface 

 and the deepwater. The Swedish expedition in august 1907 to the Belts 

 and Oresund, first discovered the submarine semidiurnal waves which 

 for the last 4 years have been registered daily at the Marine Sta- 

 tion on Borno. 



As director of the work of Svenska Hydrografisk-Biologiska 

 Kommissionen, I have been able to concentrate my attention on these 

 problems and to obtain expert help in such questions of astronomy 

 and mathematics, as are beyond my own reach. Reports by the 

 experts J. W. Sandstrom, N. Zeilon, H. Pettersson, G. Stromberg 



a. o. are published separately in Sv. Hydr.-Biol. Kom:s Skrifter. The 

 material compiled from selfregistering instruments and from the 

 analytic work of our assistant V. Soderberg is too large to be pub- 

 lished in extenso. All observations, however, are recorded in the 

 archives of the Station of Borno and are available to experts. 



In publishing this paper I have to acknowledge the aid of nume- 

 rous contributors. The historic dates I have obtained partly by stu- 

 dying original authors, partly from personal communications both 

 verbal and by letter from historians, archeologists, and philologists 

 in this and other countries. It is impossible to enumerate all those 

 from whom I have obtained information. I shall, however, always 

 give the name of my informant when making use of a statement 

 and I wish here to express my grateful acknowledgement of the in- 

 formation so courteously and readily given. 



Cosmic Causes of Climatic Variations of Short Periods. 



As mentioned in the introduction, the floods on the North-Sea 

 coast are among the events on which the mediaeval chronicles 

 put the greatest stress. In the last centuries these seem to have been 

 of an unprecedented violence and much more frequent than now. 

 The devastating force of the flood is governed by two agents, i. e. 

 high water-level and force of wind. It is impossible to ascertain 

 now whether the wind-force was greater in those ages, but it is beyond 

 doubt that the water-level on some occasions and especially in winter 

 was abnormally high and at other times much below the average, 

 or in other words, that the range of the tide attained an absolute 

 maximum in those centuries. This assertion is borne out by the 

 following facts. 



The tide-generating force of the sun and moon, which governs 

 the range of the tide, increases in our latitudes with their declination 

 and proximity to the earth and is greatest when each of the heavenly 

 bodies attains its maximum of declination and proximity to the 

 earth simultaneously. 



This happened as to the sun about 1328 (Bohlins calculation) 

 when the perihelion of the earth and the wintersolstice occurred 

 on the same day. At the time of the winter-solstice 600 years ago 

 the tide-generating force of the sun must have had an absolute ma- 

 ximum. 



The node and apside line of the moon's orbit coincide (on an 

 average) on a certain day every third year. At present that day 

 is approximately the 26th of September. In 1796 it was the 19th 

 of October and at the end of the 14th century it must have coincided 

 with the winter-solstice. The figure 1 represents schematically the 

 position of the moon's orbit at wintersolstice during a 9 years period 

 at the end of the 14th or beginning of the 15th century. It is evi- 

 dent that in all probability the moon (at newmoon), at least every 

 ninth year, attained a position nearer to the sun at winter-solstice 

 than it has since attained or will attain for thousands of years to 

 come. At fullmoon both sun and moon approached nearer to the 

 earth than usual thereby increasing their disturbing influence on its 

 gravitation. 



The position of the moon's orbit with the apside-axis pointing 

 to the sun is indicated by the ellipse. Three years later the apside- 

 axis has revolved 3 x40°645 = 121°935 (40°645 annually) in the 

 one direction and the node-axis 3 xl9°355 = 58°065 (19°355 annu- 

 ally) in the other direction. Thus they again coincide forming a 

 node-apside in the position ani. Six years later the node-apside 

 will assume the position ctvi, and after nine years the position ctjx. 

 In this position, however, the node-apside no longer points straight 

 to the sun at perihelion. It now forms an angle of 5°7 with its 

 original position at perihelion nine years ago, 18 years later the 

 angle will be 11 °4, after 36 years 22°8 a. s. o. 



Evidently a constellation like that represented by position cti 

 offers the greatest chance that the moon revolving in its orbit will 

 approach nearest to the earth and exercise its greatest influence simul- 

 taneously with the sun (at the earth's perihelion). In this constella- 

 tion the maximum of the tide -generating force will occur at fall-moon. 

 The disturbing influence on the sun's photosphere and corona, exer- 

 cised by the moon and earth together, will attain its maximum at 

 newmoon. Both maxima are absolute and will not regain their full 

 force till 2 thousand years have passed, though in the meantime secon- 

 dary maxima will appear. The situation may be described as peri- 

 helion-node-apside. 



According to a rough calculation I made, the last occurrence 

 of perihelion-node-apside ought to have taken place 1369. The in- 

 terval does not quite amount to 2 000 years. In order to get the 

 time and period more accurately determined I requested Mr. Strom- 



berg, assistant to the Observatory of Stockholm, to revise my cal- 

 culation using the latest values of the lunar constants. I also request- 

 ed Dr. Hans Pettersson to calculate quantitatively the variation 

 of the disturbance in the gravitation. 



191Z 1?&L 

 ' + Oct. 



Fig. 1. 



The calculation of Mr. Stromberg gave the year 1433 a G. as 

 the year of perihelion-node-apside. 



The report on the variation by Mr. Pettersson is published in 

 the »Publications de Circonstance » of the International Council for 

 the Study of the Sea and is called »Longperiodic Variations of the 

 Tide-generating Force ». According to the researches by Stromberg 

 and Pettersson the absolute maximum of the tide-generating force 

 must occur about 3 500 b. C, 1 900 b. C, 250 b. C. 1 433 a. C, 

 3 300 a. C. o. s. o. or with an interval of about 18 centuries (the 

 intervals are not quite equal). 



The secondary maxima which occur in the intervals between abso- 

 lute maxima are more or less developed in proportion to their distance 

 from an absolute maximum. Their appearance is regulated by the 

 occurrence of the constellations node-perihelion and ap side-perihelion. 

 These coincidences occur at intervals varying between 84 and 93 

 years ( = secondary maxima). The coincidence will be less perfect 

 every ninth year (= tertiary maxima). Finally the proximity of 

 the apside-hne to the line earth-sun at perihelion will cause the 

 tidegenerating force to attain still weaker maxima in the interval 

 between two tertiary maxima, viz. between the 4th and 5th year 

 before or after a tertiary maximum. 



The amplitudes of these different periods are approximately 

 calculated 



for secondary (84—93 years period) 2,0 °/ GO 

 For tertiary (9 years period) 2.1 °/ DO 



when taking as unit the value of the force at the absolute ma- 

 xima. 



In calculating these values, the exentricity of the lunar orbit 

 is assumed to be constant. The exentricity, however, is affected by 

 the sun and is greatest when the apsi de-line coincides with the di- 

 rection towards the sun and greatest of all when the apside-line at 

 the earth's perihelion coincides with the direction of the major-axis 

 of the earth's orbit. The absolute maxima therefore are noted by 

 a high exentricity of the lunar orbit and are strengthened by the 



