18 DISPLACEMENT INTERFEROMETRY BY 



7. Direct observations. The first experiments were made upon objects 

 lying across the campus of Brown University, since these distances, though 

 relatively small, were measurable. Unfortunately there were few available 

 long clear stretches, and distances of two objects at ^ = 9,990 cm. and 3,060 

 cm. were used. They were not, of course, in the same straight line, so that 

 the constant small angle between them must be borne in mind. The con- 

 stants of the apparatus were also correspondingly small (as it was necessary 

 to look out of a window), being b = 51.8 cm., 2^ = 9.4 cm., obtained by pass- 

 ing a beam of collimated sunlight through the system of mirrors and measur- 

 ing the length and breadth of the ray parallelogram. The angle of incidence 

 was i = 4$. Hence, since d = bR/2 cos * AAT = F/AAT, the factor is 



F = bR/2 cos 4 = 172. 2. 



It is first necessary to get AJVo, the micrometer position for parallel rays, 

 as the plate mirrors were common plate glass. This is done by inverting 

 the equation, since &N=F/d and &N' = F/d r for the two objects. The results 

 were AJV = o.oi723 cm., AJV' = o. 05626 cm. Hence the computed equivalent 

 of the angle between the two objects is &N' AN = 0.03 903 cm. (computed). 

 The value directly observed in the interferometer was AA/ 7 A]V = o.O389 

 cm. (observed), a very satisfactory agreement. Here it is to be carefully 

 noted that the fringes in the second measurement A AT, must be placed in 

 coincidence with the displaced image of the first object, not with the coinci- 

 dent images of the second object, in which case the micrometer reading 

 (AA^' = o.o4ii cm.) would be too large, or with the actual direction of the first 

 object (non-reflected beam K), in which case the reading (&N' = 0.0368 cm.) 

 would be too small; for the two objects are not in the same straight line. 

 This is of course very important, even if the angles are small. 

 We now have 



AW AJVo = o.oi723 cm. A./V' AA/o = 0.05626 cm. 



where AN = 0.0459 and AJV = 0.0839 are the observed values. Thus 

 AAf = o.o277 cm. and the practical equation now reads 



d = bR/2 cos* (AJV-AJVo). 

 Inverting the operation, we thus find 



First object, observed: AAT = 0.0450 cm., d = 9,992 cm. (computed), 



^ = 9,990 cm. (observed). 

 Second object, observed 0.0339 cm., 3,063 cm. (computed), 



3,060 cm. (observed). 



The constant AA/o is independent of the fatcor F. Hence the base b and R 

 may be changed at pleasure, from the exceptionally small value 51.8 cm. 

 here used. Finally, for this small base b of but about half a meter the micro- 

 meter play between d= 10 meters and infinity would be (A7V AJVo = 



d= 10 meters A N = 0.172 cm. 



d = kilometer, A JV = 0.0017 cm. 



