On the Theory of Equations of the Fifth Degree. 197 
We know that a stretched string which on being struck gives 
out a certain note (suppose its fundamental note) is capable of 
being thrown into the same state of vibration by aérial vibra- 
tions corresponding to the same note. Suppose now a portion 
of space to contain a great number of such stretched strings, 
forming thus the analogue of a “ medium.” It is evident that 
such a medium on being agitated would give out the note above 
mentioned, while on the other hand, if that note were sounded 
in air at a distance, the incident vibrations would throw the 
strings into vibration, and consequently would themselves be 
gradually extinguished, since otherwise there would be a creation 
of vis viva. The optical application of this illustration is too 
obvious to need comment.—G. G. S. 
XXVI. Observations on the Theory of Equations of the Fifth 
Degree. By James Cockis, M.A., F.R.A.S., F.C.P.S. &c.* 
[Concluded from vol. xviii. p. 510.) 
75. ge ee the Eulerian or Bezoutian formule to the 
trinomial, and eliminating c and d, we find (compare 
art. 44, note) 
b+ +923 —Qab?—9a'b + S8a=0,. . . . . s (e) 
$0266 + ab4—392a5}3—S402—S3at=0, . . . . - EY) 
ab! 4 208007 + (a!°—10QSa° + Ha? +9°)b° | (a! 
+ 20S4a4b?— 95a? =0. J 4 
76. Form the equation 
5 
(- 2124 20-85 -= (e!) + (f) =0; 
the result, cleared of fractions, is 
— (Ba! + 2QSa° + 39°)3763 + (Qa! + Q*3a° + QS>— S4a°)a?b? 
+ (a!°—QSa° + 29°) Satb — (2a)° + QSa° + 5°) 38a =0. } 
77. Form the equation 
eT eS aé 
{(a& ee Vie So+a} (e') + (f!)=0; 
the result, cleared of fractions and divided by 4°, is 
(a! + QSa° + 25°) a°b? + (2a! + Q3a°+3°) 76? } 
—(Qa" + Q23a° + Q3°—3540°) a*b — (a! + 2QSa° + 3°)Sa*=0. 
* Communicated by the Author. 
Phil. Mag. 8, 4, Vol. 19, No, 126, March. 1860. P 
