Interference Bands formed by Rays at Small Angles. 187 



rate of growth of timber trees ; and during the last summer I have made a 

 few trials of such measurements, using an adaptation of an apparatus 

 previously designed for observing the extension of cracks in buildings. 



In both trees and building cracks the rate of extension is very small, 

 though much greater in the former than the latter. 



The increase in diameter of ordinary timber trees, as shown by the 

 distance between the annual rings, varies largely with the species and the 

 surrounding conditions, ranging from less than 0"1 up to 0'8 inch per year, or 

 say from \ to 2|- (or more) inches increase of girth. If this growth were 

 continuous and uniformly spread over the year, the increase per hour would 

 be between 0-000028 and 0-00028 inch. 



Cracks in old buildings, on the other baud, may spread perhaps only at the 

 rate of an inch in 1000 years or 0-0000001 (or one ten-millionth of an inch) 

 per hour. With a good microscope there is no great difficulty in measuring 

 lengths of 0-00005 inch, so that, as far as magnitudes are concerned, the 

 hourly growth of trees could be quite well determined in this way ; but to 

 apply the necessary magnifying power in the position required would in most 

 cases be inconvenient. 



If, in place of ordinary optical magnification, interference methods are 

 employed, so that the change in the girth of the tree is measured in terms of 

 wave-lengths, much simpler apparatus will suffice ; for in this case the change 

 of the position of interference bands which are visible without, or with very 

 little, magnification takes the place of micrometer measures made with high- 

 power objectives. 



There are many ways of producing suitable interference bands, but I will 

 only mention the two which I have actually used. If two flat glass plates, 

 A and B, one of which (say B) has a straight edge, are superposed, so that 

 the straight edge of B rests on the surface of A, and if the surfaces of A and 

 B are slightly inclined to one another, and are viewed by reflected mono- 

 chromatic light incident normally or nearly so, the field will appear covered 

 with parallel and equidistant light and dark bands, parallel to the edge of B, 

 separated by intervals which are directly proportional to the wave-length of 

 the light, and inversely as the angle between the plates. 



If the angle is altered so that the (M-l-l)th band (say) occupies the place 

 formerly held by the nth band, the distance between the plates at that place 

 is altered by half a wave-length (in the case of soda light about the 

 hundred-thousandth of an inch). With suitable means the shift of one-tenth 

 of a band can be recognised, corresponding to an alteration of distance 

 between the plates of a milHonth of an inch. This is the plan suitable for 

 detecting the extension of cracks. 



