THE AID OF THE ACHROMATIC FRINGES. 67 



were put in the sheath. In this case (P in kg.), if C = 98 is the constant of the 

 apparatus, 



i o- 6 E = C/ (AAT/AP) or A7V/AP = 49 X i o- 6 



about one-half the smallest division of the micrometer, or a little over 

 one fringe (1.2), is all that may be looked for. The results with the fixed 

 offset were larger, 3 to 4 fringes ; or at the micrometer 



P = 4 5 4kg. io 5 AJV/AP=io to 30 io- 12 = o.5 to i.o 



Thus E is about one-quarter of the true value and three-quarters of the 

 displacement is apparently in the apparatus. Under lower loads the con- 

 ditions are not essentially different. I obtained in the triplets, for instance, 



P=i 2 i kg. io 5 A./V/AP = 33 to 50 io- l2 E = o.2 to 0.3 



largely influenced by errors in setting the micrometer, and the increased 

 uncertainty of the seat of the rod. 



The fixed offsets (ss, figs. 45, 46) were now removed and replaced by the 

 loose offsets with conical plugs and sockets (figs. 28, 34). Observations were 

 made in triplets as before, showing 



P = 4 5 4kg. io 5 A./V/AP = 33 to 34 io- 1<2 E 0.23 to 0.30 



i 2 i 27 to 40 0.24 to 0.36 



These results are identical and substantially the same as the preceding set. 

 In a series of decreasing pressures I found 



P= 5 kg. 4 kg. 3 kg. 2 kg. i kg. 



io 5 A/V/AP=i95 iS5 125 75 o 



IO~ l ~E = O.24 O.32 O.2O O.I3 



so that it is not until all but 2 kg. are removed that the apparatus registered 

 a yield or dislocation of seat. In case of the loose pulley there was no flexure 

 of the bar F; the slit-images remained in coincidence, and the fringes strong 

 and clear at all loads, without changing their inclination. Hence, since the 

 above mean AA/"/AP = 0.0003 7 cm., and as x = EAN/io l * = 0.000098 cm. is 

 to be ascribed to the steel, 0.00027 cm. per kg. may be considered as yielding 

 coefficient of the apparatus; i. e., about 0.0003 cm. should be deducted from 

 all deflections per kilogram of load. 



The endeavor was now made to ascertain where this yield is to be located. 

 It was found that by loading the pulley standards b,b' (figs. 28 and 29) no 

 appreciable displacement of fringes was produced, provided the load was the 

 same on both sides b and b' '. This is the case in the above experiments. 

 On loading b or b' alone, however, the yield was quite marked, showing 

 io 5 AA/YAP = 25 in case of loads of i and 2 kg. But this non-symmetrical 

 method of loading is never used. 



In a further examination of the apparatus it was found that vertical or 

 longitudinal slight pushes on the bed-plate (tripod) were ineffective, but 

 that a cross-push, even if a mere touch, as this directly tends to change the 

 angle a of the bar F, was very appreciable. Somehow, through the inter- 



