-ÖFVERSIGT AF K. VETENSK.-AKAD. FÖRHANDLINaAR 1 901, N:0 9. 691 



The greatest value of M occurs according to (21') and (22) 



when V = m, — m„ and I" — Q , with — ^ : tlie least value for 

 ' ra 



I' = and Z" = m, — m,; , with — - . 



m 



Thus : the greatest and the least M coincides loith the greatest 

 -and the least of the convergents (4). 



For /' = I" , thus specially when /' = /" = O , with other 

 words in the latter case when all the roots have unity as mo- 

 dulus, we have 



M = '"i "*" ^^" . (23) 



2 m 



When the equation (10) has an even number of roots, the 

 inodulse of which are not unity, and araongst these the modulus 

 of one root always is the inverse of the modulus of another, 

 then the formula (23) hoids good. Particularly this occurs when 

 the equation (10) is reciprocal. 



When the right member of the equation (6) consists of two 

 terms we have an excellent example for illustrating the last 

 three results gained, as they are all here represented. 



In this case assuming 



IAI>M2|, (24) 



the modulae of all the roots are less than unity and therefore 



M = '^. (24') 



■m 



On the contrary if 



JAKM2I (25) 



the modulffi of all the roots are greater than unity and thus 



M='^. (25') 



m 



Finally if 



\A\ = \A\ (26) 



