Effect of a Prism on Newton s Rings, 315 
For short coils we have also the alternative series given 
in (18). We find then 
+m+um « 
By using an expression for L in terms of elliptic integrals 
and expanding, Coffin * has obtained a series for L with 
which (32) agrees ; Coffin's series was evaluated up to terms 
in (A/a) 8 . Instead of using one such complicated series, it 
seems that the two series (31) and (32) should cover between 
them all the cases that occur in practice. 
XXXIII. Effect of a Prism on Newton's Pings. 
By Lord Rayleigh, O.M., Pres.P.S.\ 
TT7HEN Newton's rings are regarded through a prism 
▼ Y (or grating) several interesting features present them- 
selves, and are described in the " Opticks." Not only are 
rings or arcs seen at unusual thicknesses, but a much 
enhanced number of them are visible, owing to approximate 
achromatism — at least on one side of the centre. The first 
part of the phenomenon was understood by Newton, and the 
explanation easily follows from the consideration of the case 
of a true wedge, viz. a plate bounded by plane and flat 
surfaces slightly inclined to one another. Without the prism, 
the systems of bands, each straight parallel and equidistant, 
corresponding to the various wave-lengths (X) coincide at 
the black bar of zero order, formed where the thickness is 
zero at the line of intersection of the planes. Regarded 
through a prism of small angle whose refracting edge is 
parallel to tne bands, the various systems no longer coincide 
at zero order, but by drawing back the prism, it will 
always be possible so to adjust the effective dispersive power 
as to bring the nth. bars to coincidence for any two assigned 
colours, and therefore approximately for the entire spectrum. 
" In this example the formation of visible rings at unusual 
thicknesses is easily understood ; but it gives no explanation 
of the increased numbers observed by Newton. The width 
of the bands for any colour is proportional to X, as well after 
the displacement by the prism as before. The manner of 
* Coffin, Bulletin of Bureau of Standards, vol. ii. p. 113 (1906). 
t Communicated by the Author. 
