45 i 



SCIENCE. 



[N. S. Vol. XXIII. No. 586. 



retrograde direction. The stand which 

 supported it was then held by the speaker 

 at arm's length, while he gave himself a 

 slow direct rotation upon his feet, thus 

 imitating the motion of a retrograde planet 

 in its orbit. By applying friction to the 

 vertical shaft, and thus introducing the 

 effect of an annual tide upon a planet, it 

 was shown that the gyroscope would slowly 

 shift its plane of motion. Its equator first 

 became inclined to the orbit, like that of 

 Neptune, and later nearly at right angles 

 to it like that of Uranus. The shifting 

 of the plane of rotation continuing in the 

 same direction, the rotation itself now be- 

 came direct, and its plane gradually ap- 

 proached that of the orbit. The inclina- 

 tion was before long the same as that of 

 Saturn, and later the same as that, of 

 Jupiter. The two planes now practically 

 coincided, and the rotation and revolution 

 were in the same direction. 



When this became the case the plane of 

 rotation had reached a position of stable 

 equilibrium, unaffected further by tidal 

 action. Reversing the direction of orbital 

 motion again shifted the plane of rotation, 

 which now also became retrograde, showing 

 that the phenomenon exhibited was a real 

 property of the gyroscope, as had indeed 

 been proved theoretically, and was not an 

 effect due to some faulty construction of 

 this particular instrument. 



Tables for the Beduction of Photographic 



Measures: Burt L. Newkirk. 



These tables are intended to facilitate 

 the transformation from standard rect- 

 angular coordinates to differences of right 

 ascension and declination as well as the 

 converse transformation, and the correction 

 for refraction, including terms higher than 

 the first order in the measured coordinates. 

 Being intended primarily for use in the 

 reduction of plates made with certain lenses 

 belonging to the Berkeley Astronomical 



Department, which cover a field some ten 

 degrees in diameter, they are applicable to 

 stars whose right ascensions differ from 

 that of the center of the plate by ten de- 

 grees or less and whose declinations differ 

 from that of the center of the plate by five 

 degrees or less, no matter what the declina- 

 tion of the center of the plate may be. 



The tables for the transformation of 

 standard rectangular coordinates into in- 

 tervals of right ascension and declination 

 and its converse are based upon Professor 

 Turner's fundamental relations: 



»j^tan (d — So) 

 tan (Z = tan S sec (a — Oo) 

 tan (a — 0(1 ) 



{ sec d - 



cos {d — 5o) 



Three tables have been constructed, giving 

 quantities A, B, C, such that, given: 



Oo, S„, {, 7], 



d — So ^ kj) — Af 



a — a„ ^ fcf sec S — C, 



d — S=B, 

 giving : 



S — d„ = d — d^— {d — S), 

 or, given : 



ao, 5o, a, S, 



d — S = B, 



k7i = d — S„ + A, 



/c| sec d= {a — Oo) + C. 



In which 



Oo, So =: coordinates of center of plate ; 

 o, S = coordinates of star ; 

 J, ?; = standard coordinates of star; 

 fc:^ scale value factor. 



The tables for the determination of the 

 refraction correction are also based upon 

 formulas of Professor Turner: 



Ax= {X — x)t, 

 Ay={Y — y)t, 



' l + !o= + y' 



In which 



