HALL, ABERRATION CONSTANT. 53 



Microscopes III and I. Microscopes IV and II. 



e" 11 



T = 'J-41" O = 180° 07 — =4.13" O = 182° 04' 



r r 



4.03 179 37 3.61 176 32 



The above values give for the means 



— " = 4.04" O = 179° 35'. 

 r 



In order to reduce an actual reading on the circle, A', to a reading A^ 

 counted at the center of the circle, we have 



A = A'— — ain (A'- O). 

 r 



10. — The Microscopes. 



These are su])ported on arms which are clamped to the brass discs de- 

 scribed in article 3. This arrangement seemed to me at first not a good 

 one, but in fact the arms do not move much, and the nadir determinations 

 agree as well as those made with other instruments. This plan of mount- 

 ing the microscoi)es I have heard criticised, however, by a number of ex- 

 perieii(<'d observers. 



To the brass discs which hold the microscope arms I had brackets 

 attached, and these brackets carry fine screws which butt against the 

 arms, making it possible to adjust them easily. 



Illumination is obtained by means of little electric lamps attached to 

 the ends of the microscopes, the light coming in at right angles to the 

 line of sight, and being reflected against the circle by a plaster of Paris 

 surface. The lamps are somewhat near the circle, but as they are lighted 

 only for an instant I think there is no danger of heating it. The light is 

 furnished from chloride accumulator cells which are charged from the 

 University lighting })lant. The microsco])es are of low magnifying power, 

 about 10. The ])ower should be considerably greater. 



• The periodic errors of the screws were found as described by Professor 

 Newcomb in the Washington Observations for 1865, by measuring the 

 interval between the parallel wires of each microscope, bringing each 

 wire near a circle division and separating it from this division by a dis- 

 tance e(iual to its own thickness. ]n this waj' the periodic errors for the 

 respective microscopes were found to be 



I - 0.062' cos u -f 0.033' sin u 



II —0.186 cos u +0.231 sin u 



III +0,004 cos u +0.0.17 sin u 



IV -0.012 cos u +0.07.5 sin u 



For clamp east I is lower inicrosco])e on north side, II is upper on north 

 side, III upper on south side, and IV^ lower on south side. 



For clamp west I is lower on south side, II upper on south side. Ill 

 upper on north side, and IV lower on north side. The microscopes 

 were taken in this way for my own convenience in recording. 



On September 19, 1899, I happened to loosen the divided head of micro- 

 scope IV, and turned it on the shank. 



The periodic error was then found to be 



IV +0.057" cos u +0.039" sin u 



On May 10. 1900, the spider lines of two of the microscopes became 

 loose, owing to the use of too much oil on the screws, the oil working on to 



