290 Lord Kelvin 



on 



on the surrounding ether outside, in the line o£ the primary 

 vibration, and against the direction o£ its acceleration, of 

 which the magnitude is 



This alternating force produces a train of spherical waves 

 spreading out from T in all directions, of which the displace- 

 ment is, at greatest, very small in comparison with tsr ; and 

 which at any point E at distance r from the centre of T, 

 large in comparison with the greatest diameter of T, is given 

 by the following expression * 



f cos t-~(ut—r), 



with ^=^ irl ^~ D \o^Q .... (10;, 



where 6 is the angle between the direction of the sun and the 

 line TE. This formula, properly modified to apply it to the 

 other component of the primary vibration, that is, the com- 

 ponent perpendicular to the plane of the paper, gives for the 

 displacement at E due to this component 



7] cos - (itt — r), 

 A, 



.,, irlW-B) ,,,, 



Wlth ^P-1-XW (11) - 



Hence for the quantity of light falling from T per unit of 

 time, on unit area of a plane at E, perpendicular to ET, 

 reckoned in convenient temporary units, we have 



P + r= \ ? r %J, D) ] V cos'g+j,') . (12). 



§ 65. Consider now the scattered light emanating from a 

 large horizontal plane stratum of air 1 cm. thick. Let T of 

 fig. 1 be one of a vast number of particles in a portion of this 



* This formula is readily found from §§ 41, 42 of Lecture XIV. The 

 complexity of the formulas in §§ 8-40 is due to the inclusion in the in- 

 vestigation of forces and displacements at small distances from T, and to 

 the condition imposed that T is a rigid spherical figure. The dynamics of 

 §§33-36 with c=0, and the details of §§37-39 further simplified by 

 taking v=oo, lead readily to the formulas (10) and (11) in our present 

 text. 



