G. H. KNIBBS. 



1 Oy /l Oy 2 ■) f/l 2\ /l 2\»_ 2 -)+etc. 



2 V 'W + A2 + 2J."^TJ + A U2~2W + \2 + W p7T)(79a) 

 continuing 4/2n, 6/2n, etc. Obviously too, in expanding, we have 

 the same number of terms, since in (79) the final terms in the 

 expansion cancel one another. By considering (74) to (79a) we 

 easily see that (79a) will satisfy the same values for p as will (79), 

 or, as has been illustrated in the graph of curves 10 and 11 

 in Fig. 3, an n ic function is satisfied when n is odd, and a (n+l) ic 

 when n is even : that is to say : — 



ordinate*. Curves 6-9 , - 0*>2 Abscissa? « p 



Curve 6.— Graph of 2/(p + 1). 



Curve 7.— Graph of [JP + (n- fc)*]/nP ; k/n = | 



Curve 8. — „ „ ; „ = t 



Curve 9. — „ „ ; ,, = <j 



Curve 10 — Five symmetrical sections : graph shews that a quintic 

 function is satisfied. 



Curve 11.— Six symmetrical sections: graph shews that a quintic 

 function only, and not a sextic is satisfied. 



Prop. (o). When the transverse sections include the terminal 

 sections, are equidistant, and have assigned to them suitable weight- 

 coefficients, the coefficient being the same for any pair of sections 



