July 2, 1891] 



NATURE 



211 



The acceleration towards the sun is expressed by 



and integrating, 



^/-A 

 d^ 



+ S. 



A„9 



i'^- = 2SA 

 Substituting and reducing. 



Hence the vis viva lost, owing to the resistance of the 

 medium, is one-half of the vis viva gained by falling through 

 (•Ao - ht) towards the sun, and the presence of a very slightly 

 resisting medium increases the velocity of the earth in its orbit. 

 This increase is easily expressed, since, by Kepler's third law, 

 we may replace (A„/A,)3 by (T jT,)-, where T„T, are the periodic 

 times at the beginning and end of the period ; 



—'{©'-■!• 



But the vis viva lost owing to the resistance is equal to the 

 wor'k done in forcing the sphere against the resistance of the 

 medium through the distance passed over by the earth during 

 the time. We may assume for simplicity that during the last 

 2000 years the length of the year has shortened by five seconds ; 

 and since the change in the radius vector would be very small, 

 that A = 23300a, where a is the radius of the earth, and 

 hence that the distance through which the earth has passed is 



27r 23300a 2000. 



M. Him, by theory and experiment, shows considerable 

 reason for believing that the formula of Hutton, for the resist- 

 ance of a medium in terms of the density S, gives a result not far 

 from the truth. Hence 



•0451 X (ira-)^-i X Sxz/y-x 



27r 23 xooa 2000 ■ 



2 



{(^;/-}. 



31558150/ 9467445* 



(log-^ 14-32278) X ^"-rt-VA, 



where A is the absolute mass of unit volume of the material of 

 the earth. 



•• 1=5-64 



10^* cubic feet. 



M. Hirn further points out that this decrease of five seconds 

 in the length of the year during a period of 2000 years would 

 be accompanied by a change in the longitude of the earth of 

 more than 205", an amount quite inadmissible since the time of 

 Ilipparchus, while the above results have shown that, to pro- 

 duce an acceleration so small as this, the medium must have a 

 rarity such that one pound occupies 564 billiops of cubic feet. 

 And the volume occupied by a pound of the gas very nearly 

 varies inversely as the number of seconds gained in the periodic 

 time. 



When we pass on to consider the retardation caused by the 

 action of meteorites, we lose the guidance of M. Hirn, but are 

 able to refer for data to Prof. Lockyer's treatise. 



About 30 miles, or 158,400 feet per second, may be taken as 

 the average velocity of meteorites (p. 68). Suppose the earth at 

 rest, and struck by a meteorite weighing one pound with this velo- 

 city, the vis viva of the blow would be ^^( 158400)- = 3 '98 x lo^ 



absolute foot-pounds (p. 64). 



But the earth is moving in its orbit with a velocity of 18 "4 



miles, or 97,130 feet per second ; hence, of every three meteor- 



<>s we may presume that two strike the front, and one the back 



niisphere. Further, the velocity of the earth is, in the one 



<e, to be added to, and, in the other case, subtracted from, the 



Velocity of the meteorites. Again, we may assume that the 



earth is struck about equally all over each hemisphere, and that, 



owing to its attraction, the blows are vertical, and hence that 



the energy added and subtracted in each hemisphere in the 



direction of the motion of the earth is one-half of the total 



7 J 7-!va, or for three meteorites, each weighing a pound, 



'^ {{158400 -1- 97130)2 - 4(158400 - 97130)2} 



= 4-58 X i&f* foot-pounds. 



NO. I 131, VOL. 44] 



Suppose that a meteorite weighing one pound has the ispecific 

 heat 0-2, which is about double of that of iron ; to raise it from 

 -270- C. to 2coo° C, 454 units of heat are required, which are 

 equiva ent to about 454 x 44758 = 2 x 10" absolute foot-pounds 

 of work— a quantity which may be neglected, in comparison with 

 the total VIS viva of the meteorite. 



The weight of meteorites varies from tons to small speci- 

 mens (p. 19), and hence we must assume an average weight of 

 M pounds. According to Newcomb, 20,000,000 meteorites a day 

 enter our atmosphere (p. 69). We may again assume that the 

 action has continued for 2000 years, and caused a shortening in 

 the periodic time of five seconds. 



The vis viva of the impacts. 



4-58 



ro« X ^^^^ X 365 X 2000, 



must be equal to the vis viva lost by the earth, 



, which is W_J<_!o;86 X (97,30)-. 





6 X 946744s 



1*95 X io33 



1-115 '■< 10'" X 2000 X 9467445 

 = 9240 pounds, or over 4 tons. 

 In this case, also, the average mass of the meteorites varies 

 inversely as the shortening of the periodic time. Thus, if the 

 average weight of meteorites is 9 pounds, the shortening would 

 be only 0-005 second— an amount probably inappreciable. 



Sydney Luptgn. 



TBE FLOWERS OF THE PYRENEES AND 



THEIR FER TILIZA TION B Y J N SECTS > 

 'JpHE observations described in this work were made in the 

 Vallee de Luz (Hautes Pyrenees, France), in August 1889 

 and June 1890, between 900 and 2200 metres altitude. The 

 author has noticed 1801 visits, brought by 507 different insects 

 to 261 different flowers. In the list of the visits, date and 

 altitude are always noted, and in many cases particulars are 

 given about the special habits of insects in visiting fiowers. 

 Many of the mentioned insects were not before seen visaing 

 flowers. 



The contrivances by which the flowers are fertilized are de- 

 scribed for the following species : Merendera Bulbocoditim, 

 Asphodelus albus (lepidopierophilous, proterogynous), Hyactn- 

 thus amethystimis (proterandrous, adapted to long-tongued bees). 

 Iris pyrcnaica, Antirrhinum sempervirens, Linaria origani- 

 folia (adapted to bees, with special entrance for Lepidoptera or 

 Bombylidse), Linaria pyrenaica, Horminum fyrenaiciirn (gyno- 

 monoecious), Scutellaria alpina (adapted to long-tongued bees, 

 with special entrance for Lepidoptera), Teucrittm pyrciiaicum 

 (adapted to bees, with entrance for Lepidoptera), Diauthus 

 monspesitdamis (lepidopterophilous), Alsine sp. , Alsine vcrna, 

 Aconitum pyrenaicum (resembles the A. lycoctonum), A. 

 Anthora, Aquilegia pyrcnaica, Brassica niontana (lepidoptero- 

 philous), Roripa pyrenaica. Reseda glauca, Geranium ciucrenm 

 (proterandrous, gynodicecious), Saxifraga longifolia (proter- 

 androus), Potentilla alchemit hides, Potentilla fragariastrum. 



Some details are given about the construction of the flowers in 

 the following species : Cirsium eriophorum, C. monsptssu- 

 lanum, Cardnus medius, C. carlinoides, Centaurea Scabiosa, 

 Gnaphaliuvi Leant opodium, Angelica pyrena:a. Almost all 

 those species are illustrated (94 figures), and the explanation of 

 each figure is given in French and in Dutch. 



General conclusions : — The relative number of hemitrope Dip- 

 tera (Syrphidse, Conopidae, and Bombylidae), of allotrope 

 Hymenoptera (all Hymenoplera except the bees), of long- 

 tongued not-social bees and of Coleoptera decreases with increas- 

 ing altitude. The hemitrope Diptera (all Diptera except those 

 mentioned above) become on the contrary relatively more 

 numerous with increasing altitude ; this seems to be also the 

 case with the social long-tongued bees (represented in the 

 Pyrenees by Bombus and Psithyrus). Muller came to the same 

 conclusions about the influence of altitude upon the same groups 

 of insects in the Alps. 



/ " Dc Pyreneeenhloemen en hare bevruchting door insecten." 226 pages, 

 with five plaies, a French risumi, and the expLination of the plaies in 

 F'rench. In Hotanisch Jaarbotk, iil., 1891, published by the Botanical 

 Society Dodonan, in Ghent, Belgium). 



