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furnish discontinuous quantities and change their aspect according 

 to their boundaries being taken differently. 



In Buchan's general meteorological atlas no roses are projected, 

 only arrows indicating the most frequent direction without heeding 

 the force, and in the "Segelhandbuch fur den Atlantischen Ozean" 

 published by the "Deutsche Seewarte" for higher latitudes where the 

 wind is variable the use of wind-observations is entirely done away 

 with and arrows have been drawn in accordance with the course 

 of the mean isobars on account of the law of Buys Ballot, where 

 a constant angle of 68° between gradient and direction of wind has 

 been assumed. 



This short survey of the manner in which in the most recent 

 standard works this problem has been treated may show that indeed 

 there is as yet no question about a satisfactory solution, as has already 

 been observed. 



The aim of this communication is to hit upon a general method 

 of operation and representation of an arbitrary wind distribution 

 in which to the variable part also justice is done, whilst the gra- 

 phical representation has a continuous course and shows at a glance 

 the five characteristic quantities which mark each wind distribution 

 and which may be, therefore, called the luind-constants. 



The method proposed here is founded on the basis of the calculus 

 of probability, but it is important to notice that it is not at all bound 

 to it; at the bottom it is the same which is generally applied in the 

 treatment of directed quantities: distribution of masses and forces in 

 mechanics, the theory of elasticity, the law of radiation and the 

 theory of errors in a plane. 



2. A wind-observation can be represented by a point in a plane 

 such that the distance to an assumed origin is a measure for the 

 velocity of the wind (or force) and that the angle made by the 

 radius vector with the Y (North) axis counted from N. to E. indicates 

 the direction. If in this way all observations, N in number, are drawn 

 and if w r e think that to each point an equal mass is connected, then 

 in general the centre of gravity will not coincide with the origin 

 selected ; its situation may be determined by the quantities R and «. 

 The distribution of the masses around the centre of gravity, is then 

 characterized by the lengths .1/ and M' of the two principal axes of 

 inertia and the angle ,? enclosed by the axes M and Y . 



As is known the live constants by which such a system is charac- 

 terized can be calculated according to this purely mechanic notion 

 by determining the moments J/., and My with respect to the axes 



47* 



