THE OBSERVATIONS OP AIR AND SEA MOTIONS. 13 



100. Horizontal Motion and Vertical Motion. The considered observations, 

 those from the earth's surface as well as those from the higher strata, do not give 

 full information on the direction of the motion. They only give the azimuth of the 

 direction, not its inclination relatively to the horizon. Observations of the vertical 

 components of the motion are difficult. It has been proved possible lately to derive 

 the vertical velocity of the air from the motion of pilot-balloons, the observations 

 being taken in a more complete way by two theodolites and base.* This or other 

 methods of making the observations more complete are very much to be recom- 

 mended, especially also on account of the more correct values thus obtained for the 

 horizontal velocity. But even if it be possible thus to obtain valuable results on the 

 local ascending or descending currents, it may turn out difficult to arrange a suffi- 

 cient number of observations for the purpose of getting a complete picture of the 

 general vertical motion. As long as a sufficient system of observation of this nature 

 has not been organized, we shall be obliged to derive the vertical motion indirectly. 

 This can be done by proper diagnostic methods which will be developed later, 

 provided that we know sufficiently well the horizontal motion. We shall therefore 

 first examine this part of the motion as completely as possible. 



101. Direct Result of a Pilot-Balloon Ascent. Directing our attention to the 

 horizontal motion only, we shall consider the result of the ascent of a viseed balloon. 

 Table A, columns 1,3, and 4, shows the result of an ascent as given in the publica- 

 tions of the International Committee for Aeronautical Meteorology.! 



A table like this gives more detailed information on the air-motion than we can 

 use in the subsequent work, when the result of a great number of simultaneous 

 ascents are to be worked out. The contents of the table must therefore be con- 

 densed, and evidently by forming vector-averages of the air-motion for thicker sheets 

 than those appearing in table A. 



102. Vector- Averages of Horizontal Motion Formed with Height as Inde- 

 pendent Variable. As the required averages have to be found by vector-addition, 

 a graphical method will be best. From table A we derive a curve giving a geo- 

 metrical representation of the distribution of velocity in the different heights. 

 We form the numbers noted in column 5, obtained as products of the velocities, 

 column 4, into the thicknesses Az of the corresponding sheets, column 2 ; drawing 

 then in succession segments of line having the lengths represented by the numbers 

 in column 5 and the directions given in column 3, we get a polygonal curve which is 

 seen in each of the diagrams, figs. 33 and 34 (pages 15 and 1 7). The numbers added 

 in the corners represent the heights. 



Now let us mark on the curve two points, representing two heights, and let us 

 draw the chord joining them. This chord then represents the vector-sum (or the 

 vector-integral) of velocities within the sheet defined by the two points, formed with 

 height as independent variable; and dividing by the thickness of the sheet we 

 shall get the average velocity within this sheet. In each of the figures 33 and 34 a 



*See note, p. 12. 



fPublications de la Commission Internationale pour l'Aerostation scientifique, 1907, p. 358. Strassbourg, 1909. 



