68 



♦ KNOWLEDGE ♦ 



[Jtly 27, 1883. 



FLIGHT OF A MISSILE. 



By Richard A. Proctor. 



Prop. — To deternii7ie what westerly deviation is produced 

 in the case of a missile fired vertically from the equator to a 

 height li {tlie resistance of the atmosphere being neglected). 



The real cause of the westerly deflection is the action of 

 gravity during the time of flight retarding the motion 

 originally possessed by the missile at right angles to the 

 line joining the earth's centre and the point whence the 

 missile was projected. 



Let ah che part of the equator, 

 a the point whence the missile is 

 projected vertically, with velocity 

 v'2 gh, so that it reaches the height 

 h in time t^, and in time 2 l^ reaches 

 the ground again at b, the point a 

 having in the mean time been 

 carried to c, so that 6 c is the 

 westerly deviation we require to 

 determine. 



Let c' be the point in a T which 

 a body moving in the straight line 

 a T with constant velocity r would 

 reach in time 2 t^, V the point which 

 it would have reached if constrained 

 to move in the straight line a T, but 

 with its velocity in this direction, 

 V at starting, aflected by the action 

 of gravity, so that 6' c' is the devia- 

 tion we require ; for the arc a c is 

 so small that for the purpose of this 

 inquiry, the inclination of b c to aT 

 may be neglected. We also may 

 manifestly neglect the variation in the force of gravity due 

 to the varying distance of the actual missile from the 

 earth's surface. 



Suppose that in time t the body has reached the point 

 X, put « X = .T, and join C x (0 being the earth's centre). 

 Then the retarding action of gravity on the Viody at X is 



equal to ^ - (»• being the earth's radius). Hence we have — 



drx _ _ gx 



2.3 



9 ,^ 



But ad = 2vt^ 



. V < 4 vat,"- 

 :, be = — :i-!- 

 3 r 



XT (/t- T 2;7r 



JNow 9i = tL_ ; and v = 



2 P 



• b'c'=— rfli^lSrr/i^i 

 ■■ '^ "3"' T 3P~ 



the same result which was obtained by the simpler method 

 of regarding the missile after it had once left the earth as 

 travelling in an elliptical orbit around the earth's centre, 

 and subject, therefore, to the second law of Kepler. 



If the missile is projected in latitude A, it may easily be 

 shown that the westerly deviation 



IGirht, cos \ 



3P 



The mean daily motion of the air in 1882 was 306 

 miles, being 27 miles greater than the average. For the 

 month of November, the mean daily motion was 4-19 miles, 

 being 150 miles above the average. The greatest daily 

 motion was 758 miles on Nov. 4, and the least 30 miles on 

 Dec. 11. The greatest hourly velocity was 64 miles, and 

 the greatest pressure — with the chain — 29 lb., on Oct. 24. 



Remarkable Phenomenox ix Glenisla, Forfarshire. 

 — About two o'clock on the afternoon of Wednesday, the 

 11th current, the sky was very dark, and I was on the 

 outlook for thunder, when, standing at Broomhall, in 

 Glenisla, my attention was attracted by a peculiar noise, 

 similar to that produced by a train crossing a bridge. This 

 noise was very loud, and seemed at first to be distant, but 

 latterly it came quite near, and sounded like the rapid 

 discharge of musketry, with a booming sound. There was 

 no rain at this time, but a few minutes before there had 

 been a heavy fall of rain, accompanied with a thunder-peal. 

 I looked up, and saw about a mile away a large cloud 

 twisted in the form of a screw, and revolving round and 

 round at a very rapid rate. It looked like a huge column 

 of steam, and cloud, and vapour, about fifteen yards in 

 breadth, and so high that the top of it went out of sight. 

 It was narrow towards the earth, and spread out in its screw 

 form as it reached its extreme height, with huge volumes 

 of what looked like steam or smoke in its train. The efi'ect 

 was grand. It rose above the horizon, which from my 

 point of view was formed by a wooded hill on the south, 

 and gi-adually descended towards the earth. It had two 

 motions, one circular and the other forward, and the latter 

 I guessed to be at the rate of a mile in 2i minutes. It 

 seemed to be engulfing everything in its vortex, and was 

 scattering branches, and what appeared to me pieces of 

 burnt paper, but whicli turned out to be slates. The air 

 was pervaded with a strong sulphurous smell. I followed 

 the vision, which was that of a "rushing mighty wind," 

 over the other line of the horizon to the north towards a 

 mill-pond, from which it sucked up water in great 

 quantities, which appeared to be absorbed and scattered in 

 its weird-like dance. On further inquiry I found that this 

 same visitant had in this immediate neighbourhood knocked 

 down stone dykes, levelled trees, tirred a cottage, which it 

 shook, shattered its chimney-cans in a thousand pieces, and 

 scattered the zinc ridges for hundreds of yards. The fields 

 in its train are strewed with limbs of trees, slates, and 

 splintered wood, and the whole advent was so solemn as to 

 strike with terror men, women, children, and the beasts 

 which were in the field ; and doubtless others of your cor- 

 respondents will recount its story and tell its name. — 

 Dundee Advertiser. 



