30 Art. 3.— K. Hirayama : 



and denoting the smallest value of e by eo, ^/ is always positive if 



But 

 and 



by (6) approximately. Hence in the revolution of Type 1, ,.^ is 

 always positive if the condition 



''-M^-fJ 



or 



^0 s'/3 



be fulf^Ue^l. 



3 6. Since s'^ia^i+j^i is zero when the path A touches the 

 curve j(5i, and negative or positive according as the revolution 



belongs to Type 1 or Type 2, the quantity H^ is equal to — ^^ when 

 the path is in contact with B^ and is less or gi'eater algebraically 

 than— -nr- according as the revolution belongs to Type 1 or Type 2. 

 Now it has been proved that Hx increases in the revolution of Type 

 2, and in that of Type 1 if e^ is greater than a certain positive 

 value. Hence the path A recedes from the position of the contact 

 in the revolution of Type 2, and approaches to that position in the 

 revolution of Type 1 if e^ is greater than a certain positive value. 



37. To see how the librations are changed by the resistance, 

 let us find the variation of the minimum or the maximum value 

 u of cos(?. Let X and e be the values of x and e corresponding to 

 cosd=u. We have then 



s'êx—piU=0 



