356 Mr. J. Cockle on the Theory of Equations 



impressed motion is rectilinearly propagated from the moving 

 centre. Hence if 6 be the angle wliicli any radius makes with 

 the direction of the motion^ the above expressions for V and S 

 are applicable to this case if the right-hand side of the equations 

 be multiplied by cos 6. Hence it may be inferred, as above, 

 that in proportion as the motion of the small sphere tends to be 

 uniform, the value of a^S becomes insensible. If the analysis 

 had embraced the square of the velocity, no resistance would 

 have been found, because the velocities impressed by the pre- 

 ceding and following halves of the sphere are equal with oppo- 

 site signs, and consequently the pressures on the opposite hemi- 

 spheres, so far as they depend on the square of the velocity, 

 destroy each other. 



These considerations seem to justify the inference, that a 

 planet composed of discrete atoms of the kind assumed above, 

 might pass through the a3ther and put it in motion without suf- 

 fei'ing sensible retardation. Any sensible resistance of the ajthcr 

 would first become apparent in the case of a comet moving in an 

 excentric orbit with a rapidly varying velocity. As the above 

 explanation of the non-resistance of the luminiferous medium to 

 the motions of the planets essentially depends on the supposed 

 spherical form of the atoms, it is so far a confirmation of the 

 truth of the supposition. It may also be remarked that, accord- 

 ing to the principle of the coexistence of small vibi-ations, the 

 motions impressed by the atoms disturb in no respect the trans- 

 mission of light-undulations in the neighbourhood of a planet or 

 comet. 



Cambridge Observatory, 

 April 20, 1859. 



LVIII. Observations on the Theory of Equations of the Fifth 

 Degree. By James Cockle, M.A., F.R.A.S., F.C.P.S. S^c.^ 

 [Continued from vol. xiii. p. 364.] 

 34. T ET us apply the foregoing discussion to the trinomial 



by means of the auxiliary equation 



a^+px+j}^=y. 



35. If we eliminate x, the quintic in y will be solvable pro- 

 vided the resolvent product d{y) vanishes. 



36. The development of 



e{y) = e{px + a:^)=0 



* Communicated by the Author. 



