352 C. Bancs — Contractions of Fitzgerald- Lor entz Effect. 



Art. XXX. — On a Possibility of Detecting Contractions 

 of the Order of the Fitzgerald- Lor entz Effect ; by Carl 

 Bartts. 



In my experiments on the application of the displacement 

 interferometer to the horizontal pendulum,* I came across a 

 method for measuring the linear elongation of rods, of excep- 

 tional precision and interest. In fig. 1, A, v, b, is a triangular 

 metal bracket, right-angled at a, with a vertical angle, 0. The 

 pivots, etc., of the horizontal pendulum, PP, are attached to 

 the standard v, at p andjt/, the plane of the pendulum being 

 normal to the diagram, the frame extending outward to g, 

 about a meter forward. The grating of the displacement inter- 

 ferometer is placed at g and observed along the line between 

 the concave mirrors m, n. The interferometer is linear 

 in type ; i. e. the interferometer beams mg and gn are 

 approximately in the same straight line with the frame of the 

 apparatus. A micrometer screw actuates the mirror m. Rota- 

 tions are to take place at the angles of the triangle. 



If a changes, owing to the unequal expansion of v, b, h, we 

 may write 



da = ipAJSr/2H (1) 



where ^ is the inclination of the axis, PP, of the horizontal 

 pendulum to the vertical, P (normal to the diagram) the dis- 

 tance of the grating g from the axis and AiV, the excursion of 

 the mirror n, which restores the elliptic interference pattern to 

 its fiducial position. In my apparatus i/r was usually of the 

 order of 10 -2 , P of the order lO 2 cm. 



The change of the angle, da, resulting from the elongation 

 of b, v, A, may be independently written, since a is nearly 90°, 



da = tan 0(dh/h — db/b) + cot 6(dh/h — dv / v) (2) 



If a = 45° 



da = 2dhjh- db/b-dv/v (3) 



One should notice that the equation is numerical, the quantities 

 being of dimension zero. 



To take an example illustrating equation (2), suppose 5, h 

 have the same coefficient of expansion, 7, differing from that, 

 e, of the post v. Then incorporating equation (1) 



da = (e - 7) /tan 0, or e — y = «/r tan BAN'/ 2fi 



AN is larger and the apparatus more sensitive as 6 is smaller. 

 If Aiy=10- 4 cm., R and yjr as above, 0=14° (as in my 

 apparatus) 



* This Journal, xxxvii, 501, June, 1914. 



