34 O. A. Åkef 



Hence it follows 



(14) M(t) 



From this equation T may be computed when the characteristics of the motions 

 are known. Before making this computation, we will simplify the above equation 

 by expressing M[u^) by means of the characteristics. 



Here w indicates the deviation from tlie origin. Designating the deviation 

 from the provisory mean with i and this provisory mean with ^„ , we have the 

 following relations : 



I = a* + 4^=^ + + + . 



As 



= - ü'.5, 



and according to the designation on page 24, 



(15) 



( M{i) = h; 

 Mm V3'; 



we obtain the following expressions for the desired mean values: 



(16) 



r .¥(«) = 6 — 0.5 ; 



M{u') = v; — h + 0.25 ; 



M{u^) = V3' — 1.5v; + 0.75& — 0.]25 ; 

 ^ M{U*) = — 2V3' + l.Sv/ — 0.5& + 0.0625 . 



We prefer, however, to express the above mean values in the moments about 

 the mean. Without any difficulty we obtain with the help of (4) page 24. 



(17) 



Thus all the quantities in the right membrum of (14) are computed. 



