54 MICHIGAN ACADEMY OP SCIENCE. 



the slides and touching the threads, New lines were inserted and the 

 screws were mounted in a small lathe and cleaned. Though I requested 

 that the positions of the divided heads on the shanks be carefully marked 

 this was not done, and large periodic errors were found after the return 

 of the microscopes. I think that when the instrument was made the 

 microscope heads were placed on the shanks and divided so as to elimi- 

 nate the periodic errors of the screws. Therefore I made a number of 

 attempts to find the proper positions of the heads, but was not able to 

 do it in the time at my disposal. 



For the period, then, 1900, May 10 to June 6 we have the following 

 values of the periodic errors, these being determine by measuring the 

 distance between a division and a well defined speck of dirt found on the 

 circle, rather a better method, I think than the one spoken of above: 



I —0.576" cos u —0.288" sin u 

 II -0.280 cos u— 0.738 sin u 



III —0.147 cos u —0.047 sin u 



IV +0,026 cosu+O.OJO sin u 



After 1900, June 6, we have for microscopes I, IF and IV 



I +0.036" cos u -0.502" sin u 



II —0.052 COSU-4-0.0U sin u 



IV +0.014 cos u +0.107 sin u 



In the case of III we have after Juue 6, 1900, and before July 14, 1900 



III +0.532" COS u +0.352" sin u 



After 1900, July 14 



in +0.176" COS u +0.7.58' sin u. 



In the summer of 1901 I made another determination of the periodic 

 errors which agreed with the final values as given above. 



It would he better to arrange to eliminate periodic errors, perhaps by 

 using two pairs of threads, 1.5 revolutions apart. 



The progressive errors of the microscope screws are negligible through- 

 out the interval in which they were employed. 



It requires about one day to reverse this meridian circle and readjust 

 the microscopes. 



]1. — The ColUmating Telescopes. 



These are small, having as approximate dimensions : diameter of object 

 glasses 2.094 inches, focal length 2 feet, power of eye-pieces 38, distance 

 between wyes 11.2 inches. The three screws which support ear-h tel( scope- 

 stand are at the vertices of ah equilateral triangle a side of whicli is 9.1 

 inches. Each stand is adjustable in level and azimuth. 



A number of attempts were made to obtain the flexure of the meridian 

 circle by means of the collimators, but I was never able to level them 

 with a delicate level, and finally gave it up. 



12. — Flexure. 



The flexure coefficients were determined from observations of known 

 stars, it being assumed that the effect can be expressed in the form 



ai sin z + bi cos z + ao sin 2z + b^ cos 2/., etc. 



Then calling Z the true zenith distance we have for direct and reflected 

 observations, N being the nadir reading of the circle, 



