78 



NATURE 



[May 24, 1888 



bubbles, about twice the thickness of the blue bands. The blue 

 bands are irregular and sometimes anastomose. This system is 

 similar to the veined structure found higher up the glacier. 



The second system is formed by large and regular blue bands 

 from three to six inches broad and from two to six or more feet 

 apart. This coarser system is only occasionally developed. 

 The finer system forms a well-marked synclinal curve on the 

 terminal ice cliffs, which are from 250 to 300 feet high. 



The ice here contains in places numerous angular stones, 

 principally of slate, scattered irregularly through it, and these 

 fragments always have their broad, or cleaved, surfaces 

 parallel to the smaller system of veins. These stones have no 

 doubt entered the ice through the numerous moulins and 

 crevasses which are found higher up the glacier, but as they are 

 not found in bands nor in pipes, they must have been moved in 

 position by the flowing of the ice, consequently they must 

 originally have been variously oriented, and their present 

 parallelism to the veins is a decisive proof that the smaller 

 system is due to pressure at right angles to the structure. The 

 origin of the coarser system is not so clear. I did not notice it 

 higher up the glacier, as I ought to have done if it had been an 

 older system than the smaller veins. While, on the other hand, 

 if it is a newer system the rock fragments would probably have 

 been oriented parallel with it instead of with the finer system. 



The clear blue ice is generally supposed to resist melting 

 better than the white ice, and to stand out in ridges ; but I 

 observed nothing of this on the Mueller Glacier. Both kinds of 

 ice melt here with about equal rapidity. The grooving of the 

 ice, by runlets of water, is certainly parallel to the structure 

 when that structure is vertical or highly inclined ; but the 

 grooves are formed in several layers of both kinds of ice, and it 

 seemed to me that the blue ice melted rather more rapidly than 

 the white ice. I cannot suggest any cause for this difference 

 between the ice of the Mueller Glacier and that of the Swiss 

 glaciers. F. W. Hutton. 



Christchurch, New Zealand, March 22. 



On the Rainfall and Temperature at Victoria Peak, 

 Hong Kong. 



The first column of the following table shows the month of 

 the year ; the second, the mean rainfall at the Observatory 

 (about 100 feet above the- sea) from ten years' records ; the 

 third, the mean of the past four years' fall ; the fourth, same 

 for Victoria Peak (about 1800 feet above the sea) ; the fifth, 

 the proportion between the figures in the two preceding 

 columns; the sixth, the height of ascent in feet for one 

 Fahrenheit degree of decrease of temperature (mean of the 

 past four years) : — 



1. 11. . in. IV. v. VI. 



January 1-47 2-97 463 1-56 288 



February 1 -66 2-30 3-56 1*55 305 



March 3-53 3-41 360 106 489 



April 655 789 9-19 1-16 407 



May 9-82 4-86 6-29 1-29 309 



June 1267 14-42 1671 1-16 259 



July 16-41 16-55 20*29 1*23 274 



August 16-93 i5' 2 7 I7'53 1 15 289 



September 9-89 7-98 7-01 o-88 283 



October 5-06 257 2-06 080 281 



November 1-04 0-77 1*19 1-54 267 



December 0-49 0-97 %'zi 1*25 278 



Year 85-52 79-96 93-27 1-17 310 



The rainfall at the Peak exceeds the record at the Qbservatory 

 by about one-sixth of the whole amount, and this appears to be 

 due to the circumstance that the mountain presents an obstacle 

 to the wind from whatever side it blows, in consequence of 

 which the air is forced to rise, and being thereby cooled it pre- 

 cipitates more moisture in the form of rain. Even when the air 

 is moderately dry at sea-level its temperature may be decreased 

 below the dew-point in the course of such a rife. The compara- 

 tively great rainfall in hilly districts must be attributed to this, for 

 a hill must of course exercise its influence at a distance all round. 

 Our rainfall would therefore be smaller if there were no hills 

 in this neighbourhood. But during the months of September 

 and October less rain is collected at the upper level. This is 

 explained by the circumstance that most of the rain in those 

 months is due to typhoons, when the air is everywhere as- 



cending, even above the open sea ; and the defect at the Peak is 

 most noticeable during the raging of a typhoon. The fact that 

 less rain is measured above must, however, be further investi- 

 gated. It is very doubtful whether it would not be as well to ex- 

 pose the funnels of the gauges 4 feet above the ground, where they 

 would not be so much affected by the rain drifting along the 

 surface of the earth in typhoons, as to have them 1 foot above 

 the grass, as is the case here. 



The last column of the table proves the great variability of 

 the fall of temperature with increasing height. It depends 

 upon the humidity of the air. The astronomical refraction near 

 the horizon must be affected by this, but it is rather doubtful 

 whether the effect should be ascertained by comparing observed 

 refractions with meteorological registers kept on mountains on 

 account of the condensation of moisture which tends to raise 

 the temperature on the top of the hill. But it would appear to be 

 time that some astronomer studied the refraction in connection 

 with daily weather-maps, seeing that the variation of tempera- 

 ture with increasing height is so different in cyclones and 

 anticyclones. Of course near the centre of a cyclone it is 

 scarcely possible to make astronomical observations. Bessel's 

 theory of refraction is considered a failure within 5 of the 

 horizon. Ivory's theory might possibly be made to account 

 for the refraction nearly down to the horizon by observing the 

 value of the constant /"in connection with the isobars. It, on the 

 whole, represents the variation of temperature high up in the air 

 as estimated by meteorologists. W. C. Doberck. 



Hong Kong Observatory, February II. 



Problem by Vincentio Viviani. 



To pierce in an hemispherical dome four windows such that 

 the remainder of the surface shall be exactly quadrable. It was 

 solved by Leibnitz, J. Bernoulli, and others. Viviani himself, 

 in 1692, published the construction, but without proof. Divide 

 the base of the dome into quadrants ; on the four radii as dia- 

 meters trace semi circles, one in each quadrant ; the four right 

 semi-cylinders, of which these are the bases, will pierce the dome 

 in the required windows. The following simple proof, for which 

 I am substantially indebted to Prof. Francis W. Newman, 

 would probably interest many readers of Nature : — 



OXYZ is quarter of dome ; AB, generator of cylinder meeting 

 dome in B ; BCD, plane parallel to base. Radius of dome = R = 

 OX = OB;angleCDB=:XOA = t9;DC =DB= OA = Rcos0; 

 OB . cos BOA = OA = R . cos ; .'. BOA = ; .\ arc EB = Rt? ; 



arc BC = . R cos 0. Element of surface of window is BC . ^(EB) 

 = R 2 . cos . . d0 ; .'. surface of window is the integral of this 

 from = o to = \nr. Integrating by parts, and taking limits, 

 surface of window = R 2 (%ir - 1) ; .\ the remainder of the surface 

 XYZ is R 2 , which is exactly quadrable. Q.E.D. 



Cor. The quadrable part of the quarter-dome is equal to the 

 surface of the semi-cylinder which is within the dome. For, if 

 AB = z, and arc XA=j = R0, element of surface of the 

 cylinder is z . ds = R 2 . sin . d0 ; .*. the entire surface within 

 the dome is the integral of this from = o to = ^v, viz. R 2 . 



A general discussion of Viviani's problem may be seen in 

 Lacroix, " Traite du Calcul Differentiel et du Calcul Integral, " 

 tome ii. pp. 219-22. Edward Geoghegan. 



Bardsea, May 2. 



