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Island of Saint Paul, Aleutian Islands, lat. 57° 2' N. and long. 170° W. Observed by C. P. Fish, six times a day, from August 18, 1872, to May 31, 1873, and contained in the Annual Report of the Chief Signal Officer, U.S.A., for 1873
45 68 39
5 6 2 57 40 68 77 155 44
1 40 33
3 50 20
5 50 62
3 N. 4° 35' E. .42
N. 1 28 E. .174
4 N. 73 5 W..28 S. 38 W..16
N. 38 16 W..27}
5 N. 77 18 W..32% S. 27 W. .27
N. 19 37 W..20
92 13 91 90 286 92 13 91 90 286 92 13 91 90 286
Two preceding combined.
* This addendum to page 111 was obtained too late for insertion in its proper place.
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THESE tables, and the accompanying Plates 13 and 25, are designed to elucidate the last of the series of questions proposed at the outset of this discussion, and to show the effect of combining the element of force or velocity, with that of time, in computing the mean direction of the wind. The question itself is a highly important one, for since the real point that we wish to arrive at is the mean direction and amount of the actual motion, or transfer, of the air that passes over any given place, it is obvious that if there is a difference in the velocity of winds from the different points of the compass, or over different sections of country, such as to materially affect the results that would be obtained if it were always and everywhere the same, all the computations in the foregoing pages must require correction, if they be not rendered in great measure worthless; for (where not expressly stated to the contrary) they were all made on the assumption that the velocity was uniform; or, which is the same thing, without any reference to the velocity. And, not. only so, but nearly all the observations that have ever been taken, both by land and sea, must be thrown aside (for in very few of them has the velocity of the wind been attempted to be recorded), and the whole work of observation must be commenced anew.
This question can be determined only by observation and experiment. We can know nothing about it à priori. Difference of velocity may produce a very great effect upon the mean direction, or very little, or none all. The solution of this question must therefore be viewed as vital to the search for the laws of atmospheric circulation,
The accompanying tables, collected from Series B of this work, are designed to give a synoptical view of the elements on which a determination may be based, as derived from observations taken mainly in the United States by the observers that reported to the Smithsonian Institution, in the years 1854, 1855, 1856 and 1857. The laborious work required to obtain the results here presented, was performed, under the direction of the author, by his brother, Robert A. Coffin, A.M., of Conway, Massachusetts, and other assistants, the cost being defrayed by the
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Smithsonian Institution.' Few of the observers possessing anemometers, the velocities were usually estimated in force numbers, which were reduced to miles per hour on the following scale 1. Very light breeze
2 miles per hour 2. Gentle breeze
4 3. Fresh breeze.
12 4. Strong wind.
25 5. Iligh wind
35 6. Gale
45 7. Strong gale
60 8. Violent gale .
75 9. Hurricane
90 10. Most violent hurricane
[From a monograph found among my father's unpublished writings, I extract the following statement in reference to these Velocity Tables, which were then incomplete, being in course of computation.-SELDEN J. COFFIN.
“In the Winds of the Northern Hemisphere, 1853, this question was discussed, so far as the comparatively meagre data then at my command allowed, and the conclusion arrived at was, that, as a general thing, this difference of velocity, while it increases the magnitude of the resultant, does not appreciably affect its direction. The data on this continent from which I reached the above conclusion, consisted of observations taken at 103 different places, for an aggregate period of 397 months, or about 33 years, more than half of them being from Eastern and Middle States, and only an aggregate of about two years from States and Territories west of Ohio.
"In 1857, the Secretary of the Smithsonian Institution ordered a thorough and exhaustive discussion of the subject, based on the observations reported to the Institution for the years 1854-7, from 418 different places on this continent, for an aggregate period of 8589 months, or over 700 years, in which each observer noted the direction of the wind, usually three times a day, and affixed to each record a number from 0 to 10 to represent the velocity, according to the scale given above, based on the experiments of Rouse and Smeaton.
“ The method of discussion was, first to group the places of observation into districts of moderate geographical extent, then to compute, for each district, the mean velocity of the winds, as estimated by the observers, both the lower current and that indicated by the motion of the clouds, for each of the eight principal points of the compass, for each season of the year, and for the whole year, counting all winds between the N. and E. points as northeast, those between S. and E. as southeast, etc., and finally to compute the resultant motion of each of the two currents, over each district, for each season of the year and the whole year, first from the actual motion estimated as above, and then, for the purpose of comparison, on the supposition that the winds from all directions moved with the same mean velocity. To carry out this plan required great labor, inasmuch as beside classifying the winds according to the points of the compass from which they came, the record of the estimated velocity at each separate observation, amounting in the aggregate to over three-fourths of a million, had to be translated into linear distance, or miles per hour. An aggregate of over 5 years of working time has been spent upon it. The work of classification was performed chiefly by ladies; that of translating into miles, which required only care and accuracy in applying the scale and summing up the results, by men competent for such work; while the trigonometrical resultants were mostly computed by Robert A. Coffin.
“ The results corroborate the views advanced in The Winds of the Northern Hemisphere in regard to the magnitude of the resultants, but not in regard to their direction, both of which facts will appear from the following general statements, in which it will be seen that the effect of difference in velocity is to throw the resultant northerly far more frequently than southerly, and at a much greater angle; that it increases its magnitude far more frequently than it diminishes it, and by a greater amount.
" In 10 districts north of the 45th parallel of latitude it is thrown northerly; in 9 at an average
Column I contains the name of the place of observation, to which is prefixed the zone and serial number, by reference to which on the preceding pages the reader can find the average velocity of the wind from each point of the compass for each of the seasons. See, for example, Red River Settlement; near the foot of page 148 we find, “ Mean velocity in miles per hour, Spring, North 5.32, N. E. 2.71,” etc. The places are also grouped—not as by the author, in strict sequence of latitude and longitude—but to conform as nearly as practicable to the divisions of the United States made in the “ Discussion and Analysis of Winds.”
Column II was computed as in all the tables of Series B, by having regard only to the number of observations, without any reference to velocity.
angle of 17° 32' ; and southerly in one at an angle of 8° 38', making the average of the whole northerly by 15° 13'; while it increases the magnitude of the resultant in 5 of the districts by an average of 50 per cent., and diminishes it in 5 by an average of 15 per cent., making for the whole an average increase of 18 per cent.
“ In 44 districts between the 40th and 45th parallels (exclusive of Great Salt Lake City where the results are too anomalous to be incorporated with the others), the resultant is thrown northerly in 36 at an average angle of 15° 49', and southerly in 8 at an average angle of 4' 31', making the average for the whole northerly by 12° 8'. The influence on the direction seems generally to be much greater in the western than in the eastern States of this belt, and this accounts for my failure to detect it when I prepared my former publication. The magnitude of the resultant is increased in 36 by an average of 29 per cent., and diminished in 8 by an average of 14 per cent., making for the whole an average increase of 21 per cent. In 20 districts between the parallels of 36° and 40° the resultant is thrown northerly in 17 at an average angle of 16° 36', and southerly in 3 at an average angle of 4° 11', making the average for the whole northerly by 13° 29', while its magnitude is increased in 19 districts by an average of 43 per cent., and diminished in but one, and that only by 11 per cent., making for the whole an average increase of 36 per cent.
“The near coincidence of the results in these three belts authorizes us to combine them, and we thus find that the mean influence from the parallel of 50° down to that of 36° is to render the resultant more northerly by about 13°, and to increase its magnitude about 25 per cent. This difference is not great, but may affect the general principle.
“ Through the States of Tennessee and North Carolina, from latitude 35° to 361°, the resultant is thrown northerly in 4 districts at an average angle of 18° 5', and southerly in one at an angle of 33° 57', the average for the whole being 7° 41' northerly. Most of the observations in the latter district were taken at Knoxville, Tenn., where there may be some local cause that renders the south and southwest winds so much stronger than those from the north and northwest. In each of the 5 districts the magnitude of the resultant is increased, the average increase for the whole being 40 per cent. Notice the accumulating increase of the magnitude of the resultants as we pass southerly through the 4 belts above described, viz., 18, 21, 36 and 40.
“The results in the next belt extending from latitude 30° to 35° seem perfectly chaotic. In 7 out of 16 districts the resultants are thrown northerly at angles ranging from 1° to 126°, and in 9 southerly with nearly as wide a range, the average for the whole being 3° 23' northerly. The magnitude of the resultants is increased in 7 districts and diminished in 9, the average being an increase of 2 per cent. It is within this belt that the system of westerly winds breaks up and is replaced, as we go south, by the trade wind system, and the slight degree of prevalence of the wind in any direction allows it to be controlled very much by local influences.
“Still further south out of 6 districts represented, at 5 the resultant is thrown northerly at an average angle of 17° 48'. The remaining district is represented by the City of Mexico, where the general results are in some degree anomalous, and make a longer period of observation desirable In 5 of these districts the magnitude of the resultant is increased by an average of 25 per cent., while in one it is diminished by 8 per cent. The average increase for the whole being 192 per cent."
Column III is the laborious product obtained by computing the resultants from the number of miles travelled by the winds from each point of the compass for each season. As, for example, Red River Settlement, page 148, “ Number of miles, Spring, North, 383, N. E. 38,” etc. It therefore represents time multiplied by velocity.
The remaining columns IV, V, VI and VII, are taken from the sub-tables. (See, for instance, foot-note 2 on page 148.) Column IV containing the average velocity of all winds in miles per hour, though derived from the same source as the “Mean Velocity” for the separate points of the compass, is, of course, not the arithmetical average of the latter, but was separately computed. The numbers in column V show the velocity in miles per hour in the mean direction, on the supposition that the winds from every point of the compass move with the average velocity given in column IV. These figures are obtained by multiplying the numbers in column IV by the ratios in column II. Column VI exhibits the true velocity in the mean direction, giving to the winds from the several points of the compass each their own average velocity. The results are the product of the miles per hour in column IV multiplied by the corresponding ratios in column III. Column VII represents the excess of the velocities in column VI over those in column V, as expressed by the use of the plus sign, the minus sign being employed when the figures in column V are the greater. The “Mean Resultants” for the groups of stations in columns II and III were obtained mechanically by the use of a drafting instrument, and are given to the nearest whole degree, the fractions of a degree having been excluded after the computations were made.
A DRAFT OF THESE RESULTS is found in Plate 25, where the figures in column II are drawn as arrows, flying with the wind, the length of the shaft (without the barb) being proportioned to the ratios; those in column III are similarly noted, the barb being omitted, and the greater length of the shaft conforming to the increase in the ratios over those in column II. The average velocities given in column IV are found in the vertical series in the middle of the plate, a scale of miles being attached at the left. The vertical series at the extreme right-hand of the plate contains delineations of the results in the remaining columns; column V being shown in a dotted line, column VI in a continuous line; and the intervening space, which is in most cases filled with the sign +, representing column VII. In the individual stations at the lower part of the page, the velocities were, in some cases, so great as to need changes in the scale employed, which is, therefore, recorded in the margin.
An inspection of the tables and plate shows clearly that, as a general thing, the difference in the velocity of the winds from different points of the compass affects the resultant but slightly either in direction or amount. In the United States, north of 32° N. latitude, the resultant had by noting the actual velocities (i. e., the dotted arrow) is found inclined more to the right hand, that is, it represents a direction more northerly than the unbroken arrow that represents the effect when the velocity is disregarded. The annual resultants in the former case averaging S. 89° + W. with a ratio of .261, and in the latter S. 80°+ W..227. The divergence of these