April C, 1883.] 



KNOWLEDGE 



213 



d^ur iHatt)fmatical Column. 



ABSOKPTION OF LIGHT BY AIK. 

 By Richard A. Proctob. 

 Problem. — // in 50 miles of air at uni/orm density and tempera- 

 hire 1999-20(X)(/is of the sun's raijs are intercepted, v:hat is the 

 absorption in the first yard? 



In 60 miles there are 88,000 yards. Let us suppose that p is the 

 index of absorption for one yard (in which small distance the 

 absorption ninst be ajipreciably constant) ; by wliicli is siguifiod 

 that for 100 rays which reach any point in the air column traversed 

 by the light, 100 p rays pass a yard further. Then, putting as 

 unity the light which enters the 50 miles colun\n of air, the light 

 at the end of the first yai"d is p, at the end of the second it is 

 {>', of the third p'. &<.'., and of the 88000th it is p'*"'". But only 

 one-2000th of the light remains at the end of the 50 miles. Hence 

 we have — 



p'i>™i = 1/2000 

 or2000p""*° = l 

 whence, taking logarithms, we have 



log 2000 + S8000 log p = 0, 

 -log 2000 

 orIogp= -ggooo^ 

 -3.3010300 

 ""_ 88000 



4.6090600 

 °" 88000 

 - 88000 + 87996 . 6090600 



88000 

 = 1.9999615 = log 



, 99999114 



wherefore the absorption is a yard in about 886-lOOOOOOOths of the 

 light, or roughly, about one ll,300th. 



Thus, on the assumption made, we should have in a room eleven 

 yards long (which is a tolerably long room) an absorption of about 

 1-lOOOth of the light. Or, as far as absoqjtion is concerned, a light 

 at one end of snch a room would send its rays to the other end with 

 a loss of only one in a thousand. Yet (this is for the benefit of the 

 Oxford Chronicle and Berls and Buclis Gazette only) a person trj-ing 

 to read a book at night, at one end of a room eleven yards long, by 

 the light of an ordinary parafiin lamp situated at the other end, 

 ■would find the page illuminated with rather less than P99-1000ths 

 of the light which would fall on the page if he sat only a yard from 

 the lamp. 



Tliis is a little inconsistent with the great discovery of Dr. 

 Collins Symons, which astronomers and physicists have agreed in 

 kaving so severely alone. It agrees, however — strange to say — 

 with what we find in the solar system, where the planets are so 

 unkind as to neglect Dr. Symons' discovery, Saturn's disc being 



Jositiveh- less lominous (not only as a whole, but intriusicallj-) than 

 npiter's, and Jupiter's than the Moon's, the Moon's than 

 Venus's, and Venus's than Mercury's. So contrary is nature in 

 TCgard to the theories of paradoirfsts. 



©ur Cbrss Column. 



By Mepdisto. 





SOLUTIONS. 

 Problem No. 80, by A. J. Maas, p. Ul. 

 QtoKtsq B takes Q, or K to B4 



B to B3 Q to B4 Q takes B ch K to Kt5 or (a) 



Kt to B2 mate Q to B3 mate, or (n) if 2. K to K4 



R to B6 dis ch and mate 

 if 1. K to Klor K to Q5 



R to B4 dis ch K to Q3 or (a) R takes B ch K to B4 or (a) 

 B to B6 mate 3. Q to Kt4 mate 



(a) if 2. K to B4 (a) if 2. K to K5 



Q takes B mate 3. R to B3 dis ch and mate. 



No. 81, BY G. W. Mitchell, p. 180. 



1. B to B7 



2. F takes R dis ch and mate. 



2. R to Q5 mate 



2. Q takes R mate 



2. Q toJ35 mate 



2. Kt to Q7 mate 



2. Q to K7 mate, ic. 



If KR takes Q 

 If QR takes Q 

 If R takes R 

 If R takes Kt 

 If QKt to B3 

 If KKt to B3 



PROBLEM No. 82. 



By a. J. Maas. 



(Tho Twin of No. SO.) 



Slice 





Whitb. 

 White to play and mate in three moves. 



PROBLEM No. 83. 



By C. H. Bbocklebaxk. 



Black. 



White to play and mate in tliree moves. 



REPRINT PROBLEM No. 84. 

 Black. 





I H P 



Wbiib. 



White to play and mate in three moves. 



(A test of skill in solving.) 



ANSWERS TO CORRESPONDENTS. 



•«• Please address Chess Editor. 

 M. T. Ilooton.— In Problem 79 if 1. R to B e..), B to Kt8 ch. 

 , K takes B followed bv P and R checking, and no mate in 4 



