April 4, 19 18] 



NATURE 



85 



sphere, or rather to a height where the density of 

 the air is very small, and that it must be started 

 with such a velocity that in spite of the air resist- 

 ance in the first part of its course, its remaining 

 ]'■ speed, after having reached the upper air, shall be 

 sufficient for its further progress. 



At the surface of the earth and with ordinary 

 projectile velocities (2000 to 3000 ft. per sec.) 

 the resistance of the air is large compared with the 

 weight of the shot, even for a 12-in. projectile, 

 though, of course, this ratio decreases in the pro- 

 portion of the area to the volume. 



In the absence of air resistance, elementary 

 dynamics show that if a projectile (or particle) is 

 started upwards with an inclination of 45° the 

 ranges would be as follows : — 



Initial velocity 



1000 ft., sec. 



4000 



Range 



ir6 miles 



47 

 106 



188 „ 

 296 



It is evident, therefore, that, if a gun is to 

 carry seventy or eighty miles, the shot must attain 

 a height where the air resistance is very small, with 

 a remaining velocity of between 2000 and 3000 ft. 

 per sec. 



If the temperature of the air at all heights 

 were constant, the air itself would extend to an 

 infinite height, the pressure and density being 

 connected to well-known laws. If, on the other 

 hand, the temperature decreases adiabatically 

 with the height (as is found to be the case, at 

 any rate, up to 40,000 ft. or thereabouts), there 

 is a finite limit of about seventeen miles above 

 which no oxygen or nitrogen could exist. Above 

 this height a projectile would experience no 

 resistance, but even a few miles lower the 

 resistance would be small compared with its 

 weight. 



By using graphic methods there is no difficulty in 

 ■deducing the retardation which the shot undergoes 

 in the earlier part of its flight, though these 

 methods cannot be shown in full in this short 

 article. 



I have not computed the requisite initial velocity 

 for a 9-in. shot (such as is said to have been used 

 in the German gun), but it must be of the order of 

 5000 ft, per sec. 



Data for air resistance up to this speed will be 

 found in a paper read by me before the Royal 

 Society on May 28, 1908. 



To attain this speed a long bore would probably 

 be more suitable than an extra-strong explosive; 

 at least, this is what I found to be the case in my 

 own experiments. 



In the statement given above as to ranges in 

 vacuo it has been assumed that the trajectory 

 was parabolic. In reality, of course, it is part of 

 a very long ellipse, the projectile, in fact, behaving 

 as a satellite with an eccentric orbit of which the 

 elements can be readily calculated. 



A. Mallock. 

 NO. 2527, VOL. lOl] 



CLOUD FORMATIONS AS OBSERVED 

 FROM AEROPLANES. 



THE recent development of aviation has pro- 

 vided a means of observing clouds which is 

 much superior to any hitherto known. A modern 

 aeroplane can reach the clouds in a very short 

 time, and in many cases get above them. Observa- 

 , tions of temperature can easily be obtained, and 

 probably humidity observations would present no 

 great difficulties. The "bumps" experienced also 

 give some information as to the nature of the 

 disturbance causing the formation of the clouds. 

 It is well known that the two most important 

 ! processes which cause clouds to form are (i) the 

 i mixture of layers of air of high humidity and 

 j different potential temperature, ^ (2) adiabatic ex- 

 I pansion due to upward movement. 

 ' The first process is the cause of most horizontal 

 ' cloud-sheets, and the latter of the most typical 

 j cumulus clouds and also of rain-clouds. Many 

 I clouds of cumulus and strato-cumulus character 

 I are due to both processes combined. 

 j It has not hitherto been clearly understood pre- 

 I cisely how cloud-sheets a few thousand feet above 

 I the surface are formed. Observations from aero- 

 planes show that under these cloud-sheets there 

 is always some vertical disturbance and a lapse- 

 rate of temperature {i.e. a rate of decrease of 

 temperature with height) which is little below the 

 adiabatic rate for dry air, while above the clouds 

 the air is undisturbed, and there is a marked rise 

 of temperature for a few hundred or a thousand 

 feet above the clouds. The disturbance within and 

 below the clouds is not violent in the case of a 

 horizontal cloud-sheet, and is of the same nature 

 as the eddy motion discussed by Major Taylor ^ 

 with reference to the fogs off the Newfoundland 

 Banks. The disturbance is transmitted upwards 

 from the earth's surface, and consists of a fairly 

 regular distribution of eddies, which do not last 

 long, the disturbed air soon mixing with the sur- 

 rounding air. The effect of heating or cooling the 

 air at the surface has been discussed by Major 

 Taylor, but the , type of cloud-sheet we are now 

 considering is caused rather by the movement of 

 a body of air over a wide stretch of sea where 

 there is not much change of temperature. In the 

 course of time the air up to the height of a few 

 thousand feet is thoroughly mixed, with the result 

 that the lapse-rate of temperature becomes adia- 

 batic and the relative humidity increases with 

 height; in many cases a cloud-sheet forms at the 

 top of the disturbed layer of a thickness usually 

 less than 1500 ft., often less than 500 ft. As 

 the normal lapse-rate for the atmosphere generally 

 is less than the adiabatic, there is an increase of 

 temp>erature on passing from the disturbed to the 

 undisturbed layer, which renders slow the further 

 upward penetration of the eddy motion. 



1 Potential temperature is the temperature which a specimen of air would 

 acquire if it werebroueht down, under adiabatic conditions, from the position 

 jt occupied to the earth's surface. 



- Se« (i) "R.'porton the Work carried out by the S.S. Scotia, tpi3," 

 pp. 48-68 (London, 1014), and, also bv Major Taylor, (a) " Eddy Motion in 

 the Atmosphere" {Phi/. Trans , A Series, vol. ccxv. (1915). pp. i-a6) and 

 (3) " The Formation of For and Mist " (Quarteriy Journal Roy. Met. Soc. 

 vol. xliii., No. 183, July, 1917). 



