( ^ft ) 



conditiDii that, when tlio axes of cooi-dinalcs coincide with the 

 principal axes, tJie iiioiiiciil of (JoNialioii or coilrifugal force M'\ai 

 will \'aiiish, we liiid : 



xy~ — 18°35' 

 and flirt jjei' 



M/ — (3.45 M,;- — 8.72 ^V = U.lo 



and from formida (9) 



/• =: 0.820. 



Tt ajjpears, therefore, that, in this case, all directions uf the 

 accidental qnantities are equally probable, so that we are fully 

 justitied in putting: 



r — 0.833. 



The mean and llic probable error for each group are then : 



J/ =8.89 irrr:3.24 



and the linal I'esult for each group: 



1.70 mM. . . . |)robable error 0.810 

 and for each row : 



0.055 mM. . . . i»robable eri-oi' 0.027 

 so that Ihc probable iiKH'rliliidc of the linal outcome amounts to 

 almost exactly half the amplitude. 



7. The (piestion may also be jtnt. \\\\\\\ ^vill happen if the 

 arguments of Table 1 are varied in such a mamier, thai the \ai'ia- 

 tions are equivalent to arrangements according to other periods 

 slightly dilferent from 25.8 days. 



The amount of the variation is limited by the ]iund)er of rows 

 taken together in one group, \\ liicli eau be shifted oidy as a w hole, 

 and the variation ceases to ha\e any sense as soon as the sums of 

 each grouj) would be sensibly alfected by the actual ai-rangemenl 

 according to the new pei'iod. 



If quantities, periodical williin a length of time 7', are arranged 

 according to a period T' in /// columns, the \alue at the origin of 

 time being represented by : 



A ros (\ 



the record to be inscribed in the /'•' column of the y^''' row (/and^> 

 counted from nought) will be : 



/2.T n It 



A cos I — . — — C -\- 2ji p — 

 y 7n n n 



2;r , 2jt 



