As a matter of fact, however, observations prove that the tides at the two ends of the Panama Canal differ in almost every respect. As regards time, for example, high water and low water at the Atlantic entrance are almost exactly three hours earlier than at the Pacific entrance, although the latter is the more easterly. And as regards range, the tide at the Atlantic end rises and falls a little less than a foot on the average, while at the Pacific end the rise and fall averages 12.5 feet.
But what is even more striking is that the very character of the rise and fall of the tide at the two places is different. At the Pacific entrance there are two high and two low waters each day; but at the Atlantic entrance there are frequently several days at a stretch when but one high water and one low water occur each day. This difference in the character of the rise and fall is clearly brought out in a comparison of tide curves at the two places for several days.
In Fig. 1 are shown the curves representing the rise and fall of the tide at Balboa, on the Pacific side of the canal, for the tenth, fourteenth, and eighteenth of January, 1927. The horizontal line associated/ with each of the curves represents sea level. At a glance it is seen that the rise and fall of the tide here is of a regular character, two high and two low waters occurring each day with morning and afternoon tides resembling each other in all respects. And, except for the difference in the times of high and low water, the tide curve of one day resembles that of another.
At Cristobal, on the Atlantic side of the canal, the condition of tidal affairs is quite different, as an examination of Fig. 2 reveals. In this figure are shown the curves of rise and fall at Cristobal for the same days as in Fig. 1. Here the tide is clearly not of as simple a character as on the Pacific side. Morning and afternoon tides are here generally dissimilar; the tide curve for one day is not the same as that for either of the other days; and on the eighteenth there is but one high and one low water, instead ot two as on the other days. In fact, the only apparent similarity between the two sets of tide curves is the progression in the times of high and low water. At both places the tides on the eighteenth are approximately seven hours later than on the tenth.
The rise and fall of the tide as represented by the tide curves of Fig. 1 is typical for Balboa. During any month, to be sure, the rise and fall is greater than the average at the times of new and full moon, and less than the average at the times of the moon’s first and third quarters. But the character of the rise and fall remains the same, with morning and afternoon tides resembling each other in all respects.
In the same way the tide curves of Fig. 2 are representative of the rise and fall of the tide at Cristobal. Within a week there are generally two days each with two high and two low waters, with relatively little difference between morning and afternoon tides. This is followed by two or three days in which morning and afternoon tides differ considerably; these in turn being followed by two days in which but one high and one low water occur.
The change in the character of the tide from day to day at Cristobal is found to be related to the varying positions of the moon relative to earth and sun. But before considering this matter further it will be of advantage to digress for a moment to a consideration of the tide in general. That moon and tide were in some way intimately connected, must have been discovered early in the life of mankind; for, not only does the tide vary in the amount of its rise and fall with the moon’s changing phases, but like the moon it also comes later every day by about fifty minutes. That the sun, too, is concerned in the rise and fall of the tide is evident from the fact that at times of full and new moon, when sun, moon, and earth are approximately in line with one another, the tides have their greatest rise and fall; while when the moon is in her first and third quarters, that is, when sun, moon, and earth are at the vertices of a triangle, the rise and fall of the tide is at a minimum.
Before the beginning of the Christian Era, the Greeks and Romans had recognized the fact that the tide was brought about by sun and moon, and they recognized, too, that the moon played the leading role. But the agency by means of which sun and moon produced the tide remained a mystery for many centuries. Indeed, it was not until the genius of Newton in the latter decades of the seventeenth century discovered and
FIG. 1. TIDE CURVES. BALBOA. JANUARY, 1927
formulated the law of gravitation that the connection between moon and tide received a rational explanation. Newton proved that the tides were a necessary consequence of the law of gravitation. The sun and moon in their varying positions relative to the earth bring about attractive forces which, with regard to the solid earth and the over- lying waters of the sea, are unequal. And it is these differences of attraction which give rise to the tides.
At first thought it is something of a paradox that in the tidal movement of the sea, the sun must yield supremacy to the moon which is so much smaller a body. But when on the basis of gravitation the tide-producing power of a heavenly body is developed mathematically, it is found to vary directly as its mass and inversely as the cube of its distance from the earth. In round numbers the sun has a mass 26,000,000 times that of the moon, but it is 389 times farther away. Hence the tide-producing power of the sun is to that of the moon as 26,000,000 is to (389)3 or somewhat less than half.
The moon moves around the earth in an orbit inclined to the equator; which means that part of the month the moon is north of the equator and part of the month south. The earth likewise moves around the sun in an orbit inclined to the equator, so that part
of the year the sun is south of the equator and part of the year north. These relative movements of earth, moon, and sun, together with the daily rotation of the earth, give rise to two primary classes of tide- producing forces: (1) those having a period of about half a day, which are therefore called semi-daily forces; (2) those having a period of a day, known as daily forces. Of these two classes the semi-daily tide- producing forces are the larger. They go through two complete cycles in a day and it is because of the predominance of these semi-daily forces that there are at most places two complete tidal cycles, and therefore two high and two low waters in a day.
It is important to note in this connection that the tide-producing forces are astronomic in origin, and hence are distributed over the earth in a regular manner, varying only with latitude. But the response of any ocean or sea to these astronomic tide-producing forces depends on its depth and configuration. As a result the tides as they actually occur differ markedly not only in time and in range but also in the character of the rise and fall.
With regard to character of rise and fall, tides are most conveniently divided into three types, known respectively as the semi-daily, daily, and mixed types of tide. The semi-daily type is illustrated by the tide curves of Fig. 1, the distinctive feature of this type being two high and two low waters in a day with but little difference between morning and afternoon tides. The daily type is illustrated by the lower curve of Fig. 2, the distinctive characteristic of this type being the occurrence of but one high and one low water in a day. The mixed type of tide is illustrated by the middle curve of Fig. 2, the distinctive feature being two high and two low waters in a day with considerable difference between morning and afternoon tides.
Now it can be easily shown that the mixed type of tide arises from the combination of a daily and a semi-daily tide. Suppose that at a given place the semi-daily and the daily tide-producing forces each give rise to a simple tide of their own kind with a range of two feet as shown in Fig. 3. In this diagram the dotted curve represents the semi-daily tide and the dashed line the daily tide. What will the resultant tide be like? Clearly, to derive the resultant tide all that need be done is to add the heights of the two constituent tides at various times throughout the day and draw a smooth curve through the points so determined. In Fig. 3 the full-line curve is the resultant tide curve, and proves to be of the mixed type of tide.
Parenthetically it should be noted that various forms of the mixed type of tide are found to occur. At Cristobal, for example, the difference between morning and afternoon tides is largely in the high waters. At Seattle, Washington, however, this difference is almost wholly in the low waters, morning and afternoon low waters frequently differing by as much as eight feet. A third form, in which morning and afternoon tides differ in both the high and low waters, is exemplified at San Diego, California.
All the different forms of the mixed type of tide, however, can be shown to result from different combinations of daily and semi-daily tides. In the example shown in Fig. 3, the two constituent tides were taken to have the same range and such time relations that their high waters coincided. By giving the daily and semi-daily constituent tides different ranges and different time relations, all the various forms of the mixed type of tide can be derived.
Mathematically it is not difficult to prove the following general results with regard to the combination of daily and semi-daily constituent tides. When the range of the daily constituent is less than twice that of the semi-daily, two high and two low waters will occur in a day, the difference between morning and afternoon tides increasing with the relative increase in range of the daily constituent. When the range of the daily constituent is between two and four times as great as the semi-daily, either two high or two low waters, or only one high and one low water will occur in a day, depending on the difference in phase between the two constituents. When the range of the daily constituent is more than four times that of the semi-daily, only one high and one low water will occur in a day.
It appears, therefore, that in the rise and fall of the tide at Balboa there is very little daily tide, for as Fig. 1 shows, morning and afternoon tides differ in scarcely any respect. At Cristobal, on the other hand, the daily tide appears to be relatively large, for not
mathematician, R. A. Harris, and in Fig. 4 are shown the oceanic oscillating systems as developed by Harris for the semi-daily tides.
The Roman numerals on the oceanic oscillating systems of Fig. 5 denote the lunar hours of high water over the areas indicated. Several of the oscillating systems overlap, and these are distinguished by different kinds of shading. The nodal lines about which the various systems oscillate are indicated by dashed lines across the shaded areas. The unshaded parts of the ocean are areas of such size and depth that the direct action of the tide-producing forces on these areas can produce but little tide. In these regions, therefore, the tides that occur are due to the tides originating in the neighboring oscillating areas.
A number of puzzling tidal features in various parts of the world are nicely explained by the stationary-wave theory. Applying it to the tides at Panama we see first, that the Atlantic end of the canal opens into the Caribbean Sea which is effectually cut off from the oscillating system of the open Atlantic by the girdle of islands that mark off the northern and eastern limits of the Caribbean. Furthermore, the Gulf of Mexico and the Caribbean constitute an area of such length and depth as to have a period of oscillation of approximately twenty-four hours. Hence this area will respond best to the daily tide-producing forces, and here we have the explanation of the relatively large daily constituent of the tide in the Caribbean Sea.
The basin comprising the Caribbean Sea and the Gulf of Mexico is much smaller and much shallower than the basins of the Atlantic and Pacific oceans. Hence the tides raised by tide-producing forces in the former are much smaller than in either of the latter. The Atlantic end of the canal therefore lies in a region characterized by small tides and by a relatively large daily constituent. The Pacific side of the canal, however, as a glance at Fig. 5 shows, is situated at the end of an oscillating system of the semi-daily tides. This means that the range of the semi-daily tide here must be considerable. On the basis of the stationary-wave theory, therefore, the very considerable differences in the range and characteristics of the tide at the two ends of the Panama Canal find reasonable explanation.
RUINS OF OLD PANAMA XXV
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Courtesy Chief Boatswain J. D. Thompson, U. S. Navy
SIGNAL STATION ON THE BANK OF THE PANAMA CANAL
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