282 peters: measurement of small dilatations 



conical holes, 0.5 mm. in diameter, 0.2 mm. deep, and about 

 15 mm. apart, were drilled in the lower surface of the cover plate. 

 The pins were placed between the interferometer plates so that 

 the points of the cones fitted into the holes in the cover plate. 

 These holes kept the pins in their triangular positions, stopped 

 any creep of the cover plate and served as reference marks in 

 the determination of the change in length of the pins. The 

 fringes were viewed with a Pulfrich- apparatus. With this 

 instrument the part of the interference pattern which is obscured 

 by the pins can be easily bridged with the crosswires. 



Let the lengths of the three pins be designated as A, B, C, 

 the wave length of the light as X, and the order of interference 

 between the plates at each reference mark as ai, bi, C\, under 

 one condition, and ai, bi, Co, under a second condition. The 

 absolute changes in the lengths of the pins are then : 



(i) 



(3) 



The changes in order (ao - ai), etc., can be obtained, from 

 the displacement of the fringes past the reference marks or from 

 the determination of the whole orders ai, ao, bi, etc., by using 

 the approximate length of the pins and the measured fractional 

 orders due to several wave lengths, by the method described by 

 Meggers,^ which holds as well for straight fringes as for Haid- 

 inger's rings. 



The relative or differential changes in the length of the pins 

 can be determined from the differences in order at the reference 

 marks. The quantity (ai - 61) is the difference in the orders 

 between the plates at A and B under the first condition, and 

 (a2 — 62) is the difference in the orders at .4 and B under the 

 second condition. These quantities are determined from the 

 whole number of fringes and the measured fractions, between 



2 Zeitschr fiir Inst. i8: 261. 1898. 



3 Bull. Bur. Stand. 12:203. 1915-16. 



