336 Dr. G. J. Stoney on Microscopic Vision. 



points equally spaced in a plane,, and all emitting light which 

 at each instant is exactly similar, will produce a disturbed 

 condition of* the sether which is resolvable into plane waves 

 advancing in certain definite* directions. The same is true 

 of each other point of the original objective plane with its 

 replicas. Hence, and since by the principle of the super- 

 position of small motions the total disturbance in the aether 

 caused by the whole contents of the objective field and of all 

 its replicas is the resultant produced by a simple geometrical 

 summation of the disturbances which would be produced by 

 the several points of the original field and their replicas, it 

 follows that in ultimate analysis the total disturbance is re- 

 solvable into the undulations of plane waves into which its 



* The luminous effects produced in these definite directions are maxima, 

 and they are accompanied by luminous effects produced in other directions 

 also ; but it is legitimate to leave these out of account. We are in fact 

 investigating the disturbance within a layer of limited thickness, the layer 

 "between the objective plane and the plane in which the front of the 

 objective lies ; and the luminous energy expended on any effects within 

 that layer, other than those producing the plane wave dealt with in the 

 text, can be made relatively as small as we please by increasing the 

 spacing between the replicas. 



This will perhaps be made clearer by considering the analogue in a 

 Fourier's expansion. If the first n terms of a Fourier's expansion of any 

 function be added together, they furnish an approximation to that 

 function which is nearer the larger n is, and which can be made as close 

 an approximation as we please by increasing n. Now the sources of 

 similar light p } p , p", &c, furnish a number of fans of undulations of 

 plane waves, each fan analogous to a limited number of terms of a 

 Fourier's expansion, this limited number being proportional for each fan 

 to d/X, where 8 is the spacing of p, p', p" , &c, and A is the wave-length. 

 They are therefore susceptible of indefinite ineiease by increasing 8. 

 Moreover, the fans which have the smaller number of terms become 

 rr.pidly the fainter: see the figure on p. 340, in which the closer the ruling 

 the smaller will be the number of terms of the corresponding fan. 



The outcome of these considerations is that the setherial disturbance in 

 fiont of the objective plane may be such that to resolve the whole of it 

 with absolute accuracy into undulations of plane waves would require 

 that these undulations shall spread in all (corresponding to d being in- 

 definitely large) instead of some (corresponding to d being finitej 

 directions. But, practically, a very moderate value for 8 is sufficient ; 

 ■since the approximation is carried far enough when the outstanding 

 luminous effects are too faint either to be seen by the eye or to affect a 

 photographic plate sensibly. 



Even if the closest of the replicas were much closer in than we have 

 supposed, they would not sensibly interfere with the vision of the original 

 object. Two or more diatoms seen together within the same field of 

 view do not sensibly interfere with the most satisfactory vision of each 

 of them, nor w 7 ould they if they all emitted light from their correspond- 

 ing points which was strictly the same at each instant in phase, direction 

 of transversal, and intensity. Each would still be as fully seen as our 

 eyes aie capable of seeing, notwithstanding the presence of the others. 



