370 Transactions of the Society, 



could be made to lie in one straight line, with their edges approxi- 

 mated. When this is the case, the distance s between neighbour- 

 ing structural elements can be found from the following formula : — 



N.A. 



Where \ is the wave-length of the light used for making the 

 measurements. 



The theory of the glass-plate micrometer in its application to 

 this type of measurement, has been considered in a previous 

 paper.* In the present research the values of the micrometer 

 scales were previously ascertained by comparing the readings with 

 a standard apertometer and goniometer respectively, by means of 

 a micrometer eyepiece ; the exact method is described elsewhere in 

 this Journal.! Having calibrated the scales in this way, the 

 measurement of successive small areas of diatom were very quickly 

 obtained. 



Xow the necessity of examining such small portions of the 

 valve, leads, as has been mentioned above, to two difficulties : 

 (1) the spectra formed are of very low intensity ; (2) they have ill- 

 defined borders. The first difficulty was avoided by the use of a 

 very brilliant light source, and by working in a dark room. The 

 second was rendered of little account by the particular method 

 used for making the measurements ; for it was found that two 

 diffracted pencils with edges of the same indefiniteness could be 

 placed in line with almost the same accuracy as if the edges of 

 both were sharp. A similar observation had been made previously 

 whan using the method for the measurement of absorption bands. 

 But even so it was found advisable to use an area not less than 

 10 markings wide at a time, and to use 16 wherever possible. 



The technique employed for measuring the contour of the dintom 

 valve as seen in section, depended on the relationship which exists 

 betw^een the angle of incidence of the beam of light on to the 

 grating surface, and the angle of emergence of the diffracted wave- 

 lets. The relationship may be expressed as follows : — 



If i be the angle of incidence, and cl and rf' tlie angles of diffrac- 

 tion of the beams on either side of the normal to the grating sur- 

 face, then 



Y^ = sin i -I- sin {d — i), 



and 



"— = sin {(V -f i) — sin i 



where X and D have their usual significance. 



Now it was found, although the above equations are both 



* Journ. Physiol., xliv. (1912) p. 1. f See ante, p. 363. 



