348 Lord Rayleigh : Effect of a 
If a be finite, there is no achromatic band so long as D is 
less than the value given in (9). When D acquires this 
value, the roots of the quadratic are equal, and 
1 . 
_ 1 . 
n 2 
X 
n x = 
n 2 = 
: 4a/X. 
or 
(13) 
This is the condition formerly found for an achromatic 
system of bands. If D be appreciably greater than this, 
two values of n satisfy the condition, viz. there are two 
separated achromatic bands, though no achromatic system. 
From (8) 
> h n 2 ^ 16ab/3 2 D 2 , (14) 
Thus if D be great, one of the roots, say n 2 , becomes great, 
while the other, see (10), approximates to 2a/\ that is to 
half the value appropriate to the achromatic system (13). 
There is no particular difficulty in following these pheno- 
mena experimentally, though perhaps they are not quite so 
sharply defined as might be expected from the theoretical 
discussion, probably for a reason which will be alluded to 
presently. It is desirable to work with rather large and 
but very slightly curved surfaces. In my experiments the 
lower plate was an optical "flat" by Dr. Common, about 
six inches in diameter and blackened behind. The upper 
plate was wedge-shaped with surfaces which had been in- 
tended to be flat but were in fact markedly convex. In 
order to see the bands well, it is necessary that the luminous 
background, whether from daylight or lamp-light, be uni- 
form through a certain angle, and yet this angle must not 
be too large. Otherwise it is impossible to eliminate the light 
reflected from the upper surface of the upper plate, which 
to a great extent spoils the effects. In my case it sufficed 
to use gas-light diffused through a ground-glass plate whose 
angular area was not so great but that the false light could 
be thrown to one side in virtue of the angle between the 
upper and lower surfaces of the wedge *. It will be under- 
stood that these precautions are needed only in order to see 
the effects at their best. The most ordinary observation and 
appliances suffice to exhibit the main features. 
Another question which I was desirous of taking the 
opportunity to examine was one often propounded to me by 
my lamented friend Lord Kelvin, viz. the nature of the 
* Compare " Interference Bands and their Applications," Scientific 
Papers, iv. p. 54. 
