THE AID OF THE ACHROMATIC FRINGES. 87 



The earlier observations were discarded, but even after January 14, after 

 which time the apparatus worked comparatively smoothly, instances of 

 displacement within the apparatus required readjustment. These betray 

 themselves in a lack of coincidence of the two wide slit-images (fig. 59) or 

 of the cross-wire w (the slit is really superfluous except as the collimator 

 lens may be so placed as to widen the illuminated field). This is probably 

 referable to the two supports E,E, f which change their parallelism with 

 marked changes of temperature in the room ; or it may have been within the 

 apparatus at M, N, N,'M'. It is difficult to allow for it, and a reconstruction 

 of apparatus is the only resort. 



The illuminant was an electric arc at a distance of about a meter from the 

 interferometer. This was chosen for convenience solely, as the achromatic 

 fringes can be adequately seen with a Welsbach lamp closer at hand. 



The observations will for convenience be given graphically. I merely 

 recall that the breadth of the interferometer rectangle was .R=io cm.; the 

 inclination of the pivots of the horizontal pendulum about <> = o.oi radian; 

 the angle of incidence of rays 1 = 45. Hence the change Aa of inclination 

 a of the pier will be (if AAf is the displacement of the mirror micrometer 

 and Ae of the ocular micrometer) 



Aa = ^AA r cos i/2R = 5-gX io~ 3 <pAe cos i/zR 



or 



Aa = 4 . 2 X i o~ 6 Ae rad = o . 86 X A seconds of arc 



Observations were made at about 10 a. m. and at 6 p. m. Variations of a 

 might easily have been recorded during the day, but these are not of interest 

 in their bearing on the present paper. It seemed premature, moreover, to 

 attempt the installation of photographic apparatus, as this would interfere 

 with the visual observation, which is the chief purpose here. 



In the graphic figure 61, the observations at which adjustment of slit- 

 images was necessary are marked a. 



a. This effect was always in the same direction; i. e., indicating that if no 

 readjustment had been needed the curve between January 13 and February 

 27 would have risen as a whole more rapidly than the data actually inscribed 

 show. As a mere matter of convenience the curve has been made continuous 

 irrespective of readjustments (on the average a rise of about o.i second 

 each). In this way the whole change of inclination within the 45 days of 

 observation did not exceed a second of arc and should therefore be comprised 

 within the scale of the ocular micrometer. For secondary reasons, how- 

 ever, the mirror micrometer was moved in several cases, but as the amount 

 of shift is registered on the ocular micrometer, no essential discontinuity 

 is introduced in this way. 



In addition to the reading e, the very variable temperature of the labora- 

 tory was taken and the data are inserted in the lower curve, with the values 

 increasing downward. With this arrangement the two curves show consid- 

 erable general resemblance up to about February 10. One may suppose that 



