486 



NATURE 



[June 17, 1920 



Bandung. 



9 a.m. -6 p.m. 



a Kate of 



ascent 



m. p. min. 



10 



39 

 '03 



Wind 



velocity 



n. p. sec. 



29 



37 

 23 



Also, the wind velocity scarcely ever reached the 

 values (>i5 rn. per sec.) at which, accordirig to 

 Wenger, the influence of wind velocity begins to 

 increase turbulence, so that a notable increase in the 

 rate of ascent is to be expected. 



Moreover, insolation is strongest between 9 a.m. 

 and noon ; afterwards, clouds mostly weaken it or 

 prevent further increase. , On the other hand, the rate 

 of ascent at Batavia between noon and 3 p.m. con- 

 siderably exceeds that between 9 a.m. and noon. 



Thus an explanation of the observed rates by 

 Wenger's theory practically fails ; on the contrary, 

 the supposition of vertical air movement is tenable. 



For some years I supposed that the air had to rise 

 in columns, and, the surrounding air being sucked in, 

 the balloon in most cases would also be sucked in, 

 and afterwards would not leave the ascending air- 

 columns. Later I read that J. S. Dines was inclined 

 to this conception. The criticism of this view offered 

 by Wenger must be accepted; but why should not 

 both causes co-operate in the lowest strata? 



Indeed, I have found that my results and those of 

 Wenger coincide regarding the change of rate of 

 ascent when, passing upwards, wind velocity varies. 



Denoting this change by lo^ —^-\i/ = wind velocity in 

 az 

 m. per sec, and c = height in m.), I found: 



Batavia. Thousand Islands. 



As these values show, the change of rate with wind 

 velocity is not developed strongly, the percentage of 

 ca^es in which dv/dz and A rate were of the same 

 sign being respectively for Batavia and the Thousand 

 Islands 63 and 68 only. 



Finally, we are obliged to accept the view that in 

 the sea-breeze the air must rise as the breeze dies out 

 at a moderate distance from the coast. Also, the air 

 seems to rise no higher than the sea-breeze itself, the 

 rate of rise diminishing with its horizontal velocity. 



Moreover, T think the material collected on and near 

 Java is not favourable to the idea of such a pre- 

 ponderating influence of turbulence as Wenger accepts; 

 on the contrary, it corroborates the assumption of 

 ascending columns. 



The formation of the fine-weatlier cumuli, to be 

 observed evei-y sunny day in the tropics, is clear 

 evidence of the general occurrence of these ascending 

 air columns. • W. van Bemmelen. 



On board s.s. 'Ijisondari, Pacific. 



A New Method for Approximate Evaluation of Definite 

 Integrals between Finite Limits. 



Gauss, ■ I believe, gave a very large number of 

 forms for approximate evaluation of definite integrals 

 between finite limits. His formulae are all based, like 

 Tchebycheff'S rules, on the assumption that the 

 integt-and 'is expressible approximately by a finite 

 number of terms of the series a+bx + cx^+dx^rh • • . 

 Hisi plan was to use- a minimpm. number of suitably 



NO. 2642, VOL. 105] 



weighted ordinates to give him the exact value of the 

 integral for a specified number of terms. 



Taking the range of integration to be from — i to 

 + I, which can be done without any loss of generality, 

 his simplest integral is 



where 



for 



This formula with two ordinates gives exact values 



{a + l>x+ ex* + dx^)dx, 



and is in that respect on a par with Simpson's 

 formula, which has three ordinates weighted in the 

 proportions i, 4, r, and situated at the ends and 

 middle of the range. 

 The next Gauss formula is 



|^'/(.*-yT=i{5/( -.ri) + 8/(o)-h 5/U-i);, 

 where 



This is exact up to and including the term in x" 

 in the series; Put in the same form as Mr. Merchant's 

 formula (which is also exact up to the x' term) in 

 Nature of June 3, it becomes 



ry(.r)fllr = ,V l5/(-^i) + SAr^) + sK-v,)} , 

 .' 

 where 



Xi = 0-1127, •i^2 = o'5i -f3 = 0-8873. 

 The third formula is 



flA^)dx= --| ^j_Aj{ - X,) + B/( - X,) + n/(x2) + A/(.r,)] 



where 



xi^ = =;i + f ^f , X2^ = f - f V|. 



Transferred to the other form, this becomes 



j ^1^)^-1' =o- ' 739/(-*-i) + 0-326 r/Crg) + 0-326 1/(4-3) 



-|-o-i739a(.V4) 

 where 



;ri=o'o694, .r2=o-3300, .r3=o-67oo, .r4 = o-93o6. 



This formula is exact up to and including the term 

 in x^ 



It may be noticed that although the weight factors 

 are now incommensurate, they can be written with a 

 very close degree of approximation as oil and }f, 

 and the integral then takes the form 



rj{x)dx = ^^[8/(.ri) + 1 s/(x,) + 1 Sfi-vs) + 8/(4-4)]. 

 J 



Possibly Mr. Merchant might find that this form 

 would be useful in ship design. The positions of the 

 ordinates is not sufficiently close to even tenths to 

 permit of such further modifications being made, but 

 if the ship's half-length were divided into fifteen 

 sections, the ordinates would come very near the first, 

 fifth, tenth, and fourteenth. Some of the higher 

 Gauss integrals might be found' to fit in even more 

 conveniently.' • ' Thos. Y. Baker. : 



. Admiralty Compass Ohsei-vatory, Slough, 

 Bucks, June 10. 



The Royal Military Academy. 



Sir George Greenhill in an article in N.^ture of 

 April 29, entitled " Artillery Science," passes severe 

 stricture's oh the Royal 'Military Academy— ''The 

 Shop."' These reflect on the whole staff, especially 

 the military staff, and as the officers are not permitted 



