11 8 The Rev. Professor O'Brien on the 



of weight, we may certainly conclude that the resistance de- 

 pends sensibly upon the differential coefficients of the velocity, 

 as well as upon the velocity itself. 



30. If we integrate (4.), we shall find 



d = — a e~'"^ ' cos w' t, 

 where w' = -^j 



and n-a^SllrgJ+t'. 



c 4 



Experiment shows that ^ is so small that it may be alto- 

 gether neglected in the expressions for 7i'^ ; but the part of w'^ 

 depending upon q is by no means inconsiderable, being in 

 some cases as much as half of the whole correction due to the 

 buoyancy of the medium. We see then that the time of oscil- 

 lation is only affected by that part of the resistance which de- 

 pends upon the differential coefficients of the velocity ; and this 

 proves that the resistance must sensibly depend upon the dif- 

 ferential coefficients of the velocity, since the time of oscilla- 

 tion is found to be sensibly altered by the resistance. 



31. The foregoing remarks are abundantly sufficient, I 

 think, to warrant the assumption we have been led to in article 

 19, namely, that the resistance brought into play upon the 

 vibrating aether is a linear function of the velocity and its dif- 

 ferential coefficients; and this is the only assumption that has 

 been made in the preceding papers respecting the law of re- 

 sistance. 



On the Mixture of Prismatic Colours, 



32. Before returning to the subject of the dispersion and 

 absorption of light, I shall say a few words upon the well- 

 known fact (commonly explained on the hypothesis of "three 

 primary colours"), namely, that two or more simple prismatic 

 colours, when mixed together, may produce a simple pris- 

 matic colour. The explanation of this fact, though having 

 no immediate reference to the subject of these papers, will be 

 found useful presently. We shall be very brief, and confine 

 our attention at present to one very simple case, viz. the mix- 

 lure of blue and yellow in equal intensity. 



We may represent the undulations constituting light of any 

 particular colour by the formula a cos Iniint ~ Ic .r), or more 

 simply (putting a: = 0, as we may do in the present case), by 

 the formula aaosl-nnt. The intensity is measured by a-^, 

 and the colour is determined by w, n being here the number 

 of undulations in one second. 



Let us suppose that two colours, represented by a cos 2 tt w ^ 



