182 



SCIENCE 



[N. S. Vol. XXXIV. No. 867 



of perpendicularity, giving B" = A' -]- B" -\- 

 2 cos AB. Space geometry gives B' = A' -{- 

 B' -j- C' when A, B, are orthogonal, and 

 B' = A' + B'+C' + 2 cos AB + 2 cos AG + 

 2 cos BO when that condition is removed. 



Further, space-algebra gives a complemen- 

 tary theorem, never dreamt of by either Pythag- 

 oras or Euclid. Let V denote in magnitude 

 and direction the resultant of the directed areas 

 enclosed between the broken line A -\- B -\- 

 C -\- D and the resultant line B, and let 

 sin AB denote in direction and magnitude the 

 area enclosed between A and the projection of 

 B which is perpendicular to A; then the com- 

 plementary theorem is 



4V = 2[^smAB + sin .46' + sin ^.O +} 

 -f 2|sin BC + sin BD +-^ 

 + 2|sinCI? -f } 

 -t- etc. 

 Alexander Macparlaxe 

 Chatham, Ontario 



A BRIGHT aurora OF SEPTEMBER, 1908' 



The finest display of the aurora borealis 

 seen by the writer in Omaha during the last 

 twelve years, took place on the night of Mon- 

 day, September 28, 1908. Before describing 

 its appearance, it may be of interest to men- 

 tion the weather conditions that preceded 

 and accompanied it. 



JSTo rain had fallen for about five weeks, 

 the temperature during the day time had been 

 unusually high, and strong winds had filled 

 the air with disagreeable clouds of dust. The 

 long duration of this state of the weather 

 had become very monotonous. The expected 

 clashing of a low from the northwest and of 

 a -West Indian storm from the southeast, 

 had failed to bring any relief. Another week 

 passed, and after an occasional cloudiness of 

 the sky and an increasing humidity of the 

 air had only tantalized this section of the 

 country with unredeemed promises of mois- 

 ture, the rain came at last and with it a 

 rapid and great reduction of temperature, the 



^ This escellent description was originally sent 

 to the Monthly Weather Meview, but is transferred 

 to Science, as it belongs to cosmical physics 

 rather than to climatology, to which the Monthly 

 Weather Review is now confined. — Cleveland Abbe. 



thermometer fell from the eighties in which 

 it had been hovering down to ten degrees 

 above the freezing point. Monday, the day 

 of the auroral display, opened with a tem- 

 perature of about 40 degrees and a cold and 

 disagreeable rain. It was still cloudy and 

 misty at noon, but at about three o'clock the 

 sky cleared, the wind came from the north- 

 west, and the night began with a quiet, 

 cloudless, cold and most transparent sky. 

 An occasional glance at the heavens could 

 detect no indications of an aurora. It was 

 noticed rather suddenly at about 9 :50 p.m. 

 It then appeared as an arch extending from 

 the northwest to the northeast horizon, and 

 was about 8 degrees high on the meridian. 

 Below the arch was a well-defined black 

 space of uniform tint, which might easily 

 have been taken for a bank of clouds. The 

 arch itself was of a beautiful, soft, silvery 

 whiteness, and seemed to be about 5 degrees 

 in width. Its upper limit was not quite as 

 distinct as its lower one. At this time there 

 were no streamers of any kind, nothing but 

 the arch. There was no moon to interfere 

 with the display as it was seen from the ob- 

 servatory, and the city lights were also far 

 enough away not to blind the eyes of the ob- 

 server. 



In about a quarter of an hour the scene 

 changed. A few detached streamers now be- 

 gan to make their appearance, like the soft- 

 ened beams of search lights below the horizon. 

 They were from about two or three to 20 or 

 30 degrees in length, and from one fourth to 

 about 4 degrees in width. The short beams 

 seemed to come directly out of the ground and 

 were visible against or through the black space 

 below the arch, and the longer ones passed 

 visibly even through the bright arch itself. 

 They did not seem to have any perceptible 

 lateral motion, but they all seemed to come 

 from the same vanishing point, which was 

 estimated to be about 50 degrees below the 

 horizon and on the meridian. The largest and 

 broadest streamer was in the northwest, at the 

 very end of the arch. It was about four de- 

 grees wide and 20 degrees long, and of a de- 

 cided blood-red tint. A few of the other 



