Dec. 19, 1889] 



Locusts in the Red Sea. 



I 



^■pA GREAT flight of locusts passed over the s.s. Golconda on 

 ^November 25, 1889, when she was off the Great Hanish Islands 

 in the Red Sea, in lat. 13° '56 N., and long. 42°'30 E. 



The particulars of the flight may be worthy of record. 



It was first seen crossing the sun's disk at about 11 a.m. as a 

 dense white flocculent mass, travelling towards the north-east at 

 about the rate of twelve miles an hour. It was observed at noon 

 by the officer on watch as passing the sun in the same state of 

 density and with equal speed, and so continued till after 2 p.m. 



The night took place at so high an altitude that it was only- 

 visible when the locusts were between the eye of the observer and 

 the sun ; but the flight must have continued a long time after 

 2 p.m., as numerous stragglers fell on board the ship as late as 

 6 p.m. 



The course of flight was across the bow of the ship, which at 

 the time was directed about 17" west of north, and the flight 

 was evidently directed from the African to the Arabian shore of 

 the Red Sea. 



The steamship was travelling at the rate of thirteen miles an 

 hour, and, supposing the host of insects to have taken only four 

 hours in passing, it must have been about 2000 square miles in 

 extent. 



Some of us on board amused ourselves with the calculation 

 that, if the length and breadth of the swarm were forty-eight 

 miles, its thickness half a mile, its density 144 locusts to a cubic 

 foot, and the weight of each locust yV of an ounce, then it 

 wolild have covered an area of 2304 square miles ; the number 

 of insects would have been 24,420 billions; the weight of 

 the mass 42,580, millions of tons ; and our good ship of 6000 

 tons burden would have had to make 7,000,000 voyages to carry 

 this great host of locusts, even if packed together 11 1 times more 

 closely than they were flying. 



Mr. J. Wilson, the chief officer of the Golconda, permits me 

 to say that he quite agrees with me in the statement of the facts 

 given above. He also states that on the following morning 

 another flight was seen going in the same north-easterly direction 

 from 4.15 a.m. to 5 a.m. It was apparently a stronger brood 

 and more closely packed, and appeared like a heavy black cloud 

 on the horizon. 



The locusts were of a red colour, were about 2\ inches long, 

 and ^\, of an ounce in weight. G, T. Carruthers. 



NATURE 



153 



A Marine Millipede. 



It may interest " D. W. T. " (Nature, December 5, p. 104) 

 to know that Geophihis maritinncs is found under stones and 

 sea-weeds on the shore at or near Plymouth, and recorded in my 

 "Fauna of Devon," Section " Myriopoda," &c., 1874, published 

 in the Transactions of the Devonshire Association for the 

 Advancement of Literature, Science, and Art, 1874. This 

 species was not known to Mr. Newport when his monograph 

 was written (Linn. Trans., vol. xix., 1845). Dr. Leach has 

 given a very good figure of this species in the Zoological 

 Miscellany, vol. iii. pi. 140, Figs. I and 2, and says : " Habitat 

 in Britannia inter scopulos ad littora maris vulgatissime." But, 

 so far as my observations go, I should say it is a rare species. 

 See Zoologist, 1866, p. 7, for further observations on this 

 animal. Edward Parfitt. 



Exeter, December 9, 1889. 



Proof of the Parallelogram of Forces. 



The objection to Duchayla's proof of the "parallelogram of 

 forces " is, I suppose, admitted by all mathematicians. To 

 base the fundamental principle of the equilibrium of a particle 

 on the " transmissibility of force," and thus to introduce the 

 conception of a rigid body, is certainly the reverse of logical pro- 

 cedure. The substitute for this proof which finds most favour 

 with modern writers is, of course, that depending on the 

 " parallelogram of accelerations." But this is open to almost 

 as serious objections as the other. For it introduces kinetic 

 ideas which are really nowhere again used in statics. I 

 should therefore propose the following proof, which depends on 

 very elementary geometrical propositions. The general order of 

 argument resembles that of Laplace. 



I adopt the " triangular " instead of the " parallelogrammic " 

 form. Thus, if PQ, QR represent in length and direction any 

 directed magnitudes whatever, and, if these have a single eqiii- 

 zalent, that single equivalent will be represented by PR. 



To prove that the equivalent of PQ, QK is PR. 



(i) The equivalent of two perpendicular lengths is equal 

 length to their hypothenuse. 



For, draw AD perpendicular to hypothenuse EC. 



Fig. I. 



Then, let BD, DA = k . BA, making angle e with BA 

 towards BD. 



Then, by similar triangles, AD, DC = >^ . AC, making angle 

 e with AC towards AD. 



But these equivalents are at right angles, and proportional to 

 BA and AC. Hence, their equivalent, by similar triangles, is 

 P . BC along BC. 



But BD, DA, AD, DC = BC. .: k"^ = i ; .: k = i. 



(2) If theorem holds for right-angled triangle containing 

 angle 0, it holds for right-angled triangle containing hB. 



For, let ACD = 6, where D is 90°. Produce DC "to B, such 

 thatCB^CA. ThenABD = Ae. 



Fig. 



Then assume CD, DA = CA. Add BC. . '. BD, DA'= 

 BC, CA. 



But BD, DA = BA in magnitude by (l) ; and BC, CA 

 has its equivalent along BA, •. • BC = C A. . *. BD, DA = BA, 

 both in magnitude and direction. 



(3) If the theorem holds for 6 and (p, it holds for -f <^. 1 '■- 



For make the well-known projection construction. Thus — 



Fig. 3. 



OP = OQ, QP = ON, NQ, QR, RP = OM, MP. 



(4) Finally, by (i), theorem holds for isosceles right-angled 

 triangle ; . *. by (2) it holds for right-angled triangle containing 

 angle 90° ^ 2" ; . '. by (3) it holds for right-angled triangle con- 

 taining angle ?n. 90° -^ 2" : i.e. for any angle (as may be shown, 

 if considered necessary, by the method for incommensurables in 

 Duchayla's proof). 



Hence, if AD be perpendicular on BC in any triangle, 



BA, AC = BD, DA, AD, AC = BC. 



Q.E.D. 



W. E. Johnson. 

 Llandaff House, Cambridge, November 12. 



