22 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



pendulum being supported between A and B, while the heavy base CD rests 

 on foot-screws on the cement subfloor of the basement of the laboratory. 

 BD is the brace in question, extending almost half-way up the standard at 

 an angle of about 0=14 to it. For ordinary quiet surroundings this truss 

 seemed to be adequate, as the water- vat of the float was held on a separate 

 standard, free from the pendulum and its case. The pendulum, in view of 



FIG. 15. 



FIG. 16. 



FIG. 17. 



the float, was therefore virtually very light. The difficulty encountered resides 

 in the fact that even small differences in the coefficient of expansion of BC 

 and BD will seriously tilt the axis AC. To express these relations let h, v, b, 

 be the hypothenuse, the vertical, and the base of a right-angled triangle as 

 shown in fig. 15 and idealized in fig. 16. Let </>=dh/h = db/b for the same 

 temperature increment of i C. be the coefficient of expansion of the base and 

 of the brace (for convenience), and ft = dv/v that of the brass post. Then it 

 follows easily that for an increase of i C. of the environment, 



*ty-lP|S+W fo((H-0) COS a+sin ado) 



where a: is the angle of inclination of the post and da its increment. Hence, 

 since a = 90, very nearly, 



Since tan = 0.25, nearly, 



da = $(<{' &) radians 



or, for the above a = 0.3* seconds, 



cfo = 2.7Xio 8 (0 /3) cm. 



Hence, so small a difference of coefficient of expansion as /3= io~ 6 would 

 give rise to a deflection oidx = 2.j, nearly 3 cm. per degree of increase of tem- 

 perature. In fact, this arrangement actually suggests itself as a remarkably 

 sensitive method for measuring small elongations; for, since da = ((/' p) cot 0, 

 independent of all lengths, da increases as decreases without limit, and the 

 question is merely one of experimental adjustment. If the hypothenuse h 

 alone expands, the remaining temperatures being kept constant, 



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