VOLUMES OF SOLIDS AS RELATED TO TRANSVERSE SECTIONS. 



53 



Pisr. 2. 



2-4S8 (3 Curve 538z ordinates /3 > Abscissa? =/>j * Curve Ord.=d; Absc.-£ 



6 Curves. — The ordinates denote the distance of the second section of 

 of the axis from the first and initial section — the whole axis being unity — 

 corresponding to pairs of values of the index, one series of values being 

 the abscissae. 



R Curve. — The ordinates shew the weight that must be assigned to a 

 middle section, that of the terminal sections being unity, in order to 

 satisfy any index and its conjugate. 



Prop. (j). Two terminal sections and a middle section will in 

 general satisfy the index unity together with two conjugate indices 

 the one greater and the other less than 2'Jff)8; these indices are 

 dependent upon the coefficient assigned to the middle section, which 

 coefficient can in no case be less than S-93364-7, viz., than its value 

 at the critical index 2-4-58. 



The value 1 is conjugate to 5382, corresponding to the coefficient 

 j8 = 5-174; consequently at that point p=l, q = 5 "382 and no other 

 index can be satisfied. Again if p = 1 and q = 2-458, the coefficient 

 ft will be 3-933647 and no other values can be satisfied. Again 

 2 and 3 are conjugate indices, and correspond to the weight- 

 coefficient 4 : therefore 



