Feb. 23, 1888J 



NATURE 



;9i 



is due to the error introduced into the calculations by referring 

 the impurity to the hydrogen. But, whether this explanation be 

 accepted or not, it is clear that the three lines drawn through 

 the points representing the three series of ratios ought to meet 

 at a point on the horizontal line of zero impurity, for the errors, 

 whether due to chemical action or to calculation, would disappear 

 with the cause that produced them. Hence, if no other source of 

 error is present, the true ratio may be found by taking the most 

 probable point of intersection of the three lines on the horizon- 

 tal line of zero impurity. It is not easy to determine exactly the 

 position of this point : it probably lies between the values I 996 



^ MIBUBBBU 3R3I 



■■B ■■■■itiiasHB mn 



!■■■ ■■■■■■■■■■ ■■■ 



:■■ ■■■■■■aain | 

 nailgHiiiaf-' 



we may calculate the angular radius of the bow by three different 

 methods. 



Fig. 3. 



and I -998, and the true ratio may perhaps be taken as i '997 

 Dr. Scott adopts the ratio I '994, but this appears to me to be 

 certainly a little too low. 



Prof Thorpe shows that the atomic weight of oxygen, calcu- 

 lated from Regnauit's densities of oxygen and hydrogen, corrected 

 by Prof. Le Conte, and Dr. Scott's ratio (i'994) for the com- 

 l)ining volumes, is i6'039. The ratio i'997 would make the 

 atomic weight O = 15 985. Sydney Young. 



University College, Bristol. 



The Fog Bow^ and Ulloa's Ring. 



In the summer of 1875, I made a tour of inspection to our 

 meteorological stations in the surveying-steamer Haitsteen, Capt. 

 M. Petersen, R.N. During the morning hours of August 7, I 

 was on shore at Gandfjoid, on the south side of the Varangerfjord, 

 and measured the height of some terraces there. At ih. loni. 

 p.m. we took serial temperatures in the Gandfjord with the deep- 

 sea thermometer. The weather was calm, and a dense fog pre- 

 vailed. The temperature of the air was 12" C. Leaving the 

 Gandfjord we proceeded northwards. The dense fog continued. 

 At once the fog began to be lighter and the sun to shine through, 

 and a few minutes afterwards we were out of the fog, which was 

 standing as a white wall in the south-west. In tlie moment the 

 sun appeared, but before we were quite clear of the fog, I saw 

 in the north-east a bow having the shape of a rainbow, but quite 

 white, projected on the fog. With a sextant I measured its 

 amplitude, or the chord along the horizon, and the height of the 

 summit above the horizon — in both cases the middle between the 

 outer and inner edge of the bow. The horizon not being dis- 

 tinctly visible, it is probable that the measures taken do not 

 exactly refer to the true horizon, nor is it certain that the height 

 of the summit was taken from the same horizontal plane in 

 whicli the amplitude was measured. By the captain's reckoning, 

 the apparent ship's time, at the moment of observation, was 

 2h. 40m., and the latitude 70^ i'. From these data, and the 

 declination of the sun, I computed the azimuth of the sun at 

 south 46° 5' west, and its apparent altitude at 31" 12'. Supposing, 

 as the results of the several computations tend to indicate, that 

 the white bow is circular, and has its centre in the anthelic point, 



Let // represent the height of the summit of the bow above the 

 horizon, a half the amplitude or chord along the horizon, 

 H the dip of the centre of the bow below the horizon, supposed 

 to equal the altitude of the sun, and ;- the angular radius of the 

 bow. Then we have — 



r= H -t-// (i) 



dr = dVL-^ ah (i')~ 



cos r = cos a cos H (2) 



, tana , , tan H ,,, , ,>, 



<ir = (la + all (2)' 



tan r tan r 



cos ;- = cos a cos (;- - /;) 



. I - cos a cos A ... 



tan r = , — -— , or putting 



cos a sm n 



cos a cos A = sin- M 



tan r = cot- M cot >4 (3) 



dr = cos {?■ - h) ^— 'I tan a da - sin (r - h) '^^^ dh (3') 



sm h sm n 



The observations gave za = 49°, a = 2^" 30', and ^ = 7° (or a 

 little more). 



From (i) we have r = 31° 12' + f = 38° 12'. 



Putting dR = ±2',dk = ± 15', we have by (i') 



dr - ± sji'' -f- 15- = ± I5''l = ±o°-25. 



From (2) we have r = 38° 53' '5, 



and by (2') dr = 0-577 da + 0770 dR, dH being the error in 



the altitude of the measured chord, or the chord's altitude or 



depression, reckoned from the horizon. 



Putting da = dll = ± 15' = ± o°'25, we get — 



dr = do o^'24. 



From (3) we have ^' = 41° 8', 



and by (3') dr = 2-315 da - 3-074 d/i. 



Putting da = di = ± o°'25, we get — 



dr = ± 0^-97. 



Taking the weights inversely as the squares of the probable 

 errors, we find that the results from (i) and (2) have a weight 

 of 15 times that found by (3), and the mean will be— 

 r = 38° 38' ± 6' -4. 



From this mean we find that A should have been 38° 38' - 

 31° 12', or 7° 26' instead of 7°, or somewhat greater than mea- 

 sured, as supposed in my note-book. Computing from (2) we 

 find that we should have calculated with H = 30" 51' instead of 

 31° 12', or the chord has been measured in a level 21' lower than 

 the horizon, which is highly probable with the fog spreading over 

 the surface of the sea. The measured chord being too great, and 

 the measured height too small, it follows from (3') that {3) must 

 give the radius by far too large. 



'! he next occasion I had to observe the fog bow was m 1878, 

 on the North Atlantic Expedition, when returning from Spitz- 

 bergen. During August 30, our ship, the Vdnngen, had a rather 

 tedious work in advancing southwards, on account of the fogi;y 

 weather prevailing the whole day. In the afternoon we had 

 advanced so far south of Bodo as to approach the Sandhorn, a 

 mountain about 3000 feet high, lying to the east of the route. 



At 5h. 20m. p.m. I saw an anthelic fog bow, white, with the 

 outer edge reddish, the inner edge bluish. I measured, with the 

 sextant, the amplitude along the horizon at 76 , the sun s altitude 

 at 12°, and the breadth of the bow at 2°. The teinperaiure of 

 the air was about 14° C. The latitude was about 67 10 . 



Assuming the measured chord to lie in the true horizon, we 

 get by (2) from « = 38^ H = 12°, r = 39° 35'-5- l^;'t it is 

 highly probable, that the measured chord lay deeper than the 



