Mr. Moon on the Analytical Principles of Hydrodynamics. 143 



for all the results obtained, while neglecting it entirely would 

 cause a still greater divergence between theory and observation. 



On account of the thickness of the bundle of ten plates of 

 glass, a portion of the secondary reflection would be thrown a 

 considerable distance to one side, especially when i is large, so 

 that it might fall quite outside of the instrument, or even be cut 

 off by the ends of the plates. This effect would be least marked 

 with the polarimeter, next with the Savart, and most of all with 

 the optical circle, on account of the small aperture of the tele- 

 scope. But this is just the order in which the observations 

 stand, all of them falling between the two theoretical curves. 

 These observations also show the effect to be expected from a 

 bundle of plates when used to polarize light by refraction. If 

 ten plates are employed, set, as is usual, at 57°, the polariza- 

 tion would be only 67*2 per cent, if internal reflection took 

 place, but would be 95*2 if this were in any way excluded. We 

 may in passing point out that an advantage might be expected 

 in such a polariscope from an increase in the angle of incidence, 

 the increased polarization probably more than making up for 

 the loss of light and distortion induced by the increased obliquity 

 of the incident rays. 



The want of perfect transparency of the glass would also tend 

 to increase the polarization by enfeebling the secondary reflec- 

 tion ; and dirt or grease on the^surface of the glass would pro- 

 duce the same effect. With eight or with two surfaces these dis- 

 turbing causes are much less marked, except for large angles 

 of incidence, and hence the agreement with theory much better. 



XVII. Remarks on the Analytical Principles of Hydrodynamics, 

 in Reply to Professor Challis. By Robert Moon, M.A., 

 Honorary Fellow of Queen's College, Cambridge*. 



"VT7HILE appreciating the candour evinced by Professor 

 ▼ y Challis throughout our discussion, I cannot suffer to pass 

 in silence his assertion f that my " hydrodynamical researches 

 are founded on differential equations which are really the same 

 as those employed by Mr. Earnshaw." 



Professor Challis' s argument to prove this is founded upon a 

 complete fallacy. For, taking part of my solution of the equa- 

 tion 



dt* + T>dx U ' {l) 



* Communicated bv the Author. 

 t See Phil. Mag. vol. xivii. p. 27. 



