( 23 ) 



always in the same piopoi-Hoii, hut it becomes important if this 

 proportion depends on tiie natni-e of I he problem. 



If the distribntion of errors is not independent of Ibe direction, 

 the ('oef'ticieni of y)A is deterniined by llic (piantity: 



M/ + M/ 



The eoefïicient of the probable error, for which Schols gives the 

 approximate valne : 



>■ = 0.8326 — 0.1581 A^'^ (9) 



is a maximnm for errors independent of the direction and a minimum 

 for linear errors, whe]i i\^= 1. 



By the assumption, therefore, that ail directions are equally probable 

 the most nnfavoni-able case is chosen, which, in doid^tful cases, is, 

 of course, the safest way of forming a judgment. 



Whether the operations, which are to be ajtplied to the data, are 

 considered as a determination of the first couple of constants of a 

 Fourier series (the very first, h h„, is left out of consideration), or as 

 a calculation of the average or most probable ])Osition of the end- 

 points of the vectors, or as a determination of tite situation of the 

 centre of gravity — in all cases the result is a quantity determined 

 by two coordinates and the operations we ha\e to perform are: 



l^'tiy. to se]iarate the constant part ; 



2"'^'y. if necessary to determine the situation of the axes of 

 probability ; 



o'"^'>'. to calculate the mean and probable error, in this case better 

 called incertitude. 



The same method can, of course, be ap[)lied to groups of j)eriods, 

 which gives a considerable saving of labour, but also leaves some 

 >vant of cleai'uess in the result. 



o. The investigation (^f tiie series of daily means of barometric 

 observations made at Batavia has been conducted in the same niamiei- 

 as it was commenced in 1888. The ai-rangenu^nl has been pcrlbi'ined 

 according to a period of 25.8 days, and gi'oups of 30 ro\vs have 

 been taken together so that, out of the 510 |)eriods, 17 groups have 

 been formed. 



The result of this ()|)eration is given in Table I. 



If, therefore, an oscillation, |)erio(lic in '25.8 days, really exists, 

 its amplitude is not moi'e than : 



1:^ = 0.055 mm. 

 30 



