Aug. 24, 1883.] 



KNOWLEDGE ♦ 



117 



diminishing the geometrical depression by as much as a 

 fourth or even more, sometimes by barely a sixth or even 

 less. For ordinary rough calculations it suffices to put 6 in. 

 for the optical depression due to one mile. 



It is easy to deal with any problem requiring us either 

 to find the distance of the sea-horizon for any given height 

 of the eye above the sea level, or vice-remtt to determine 

 what is the height of the eye when the sea horizon lies at a 

 given distance. For, if d is the optical depression for one 

 mile, D the depression in inches at a distance of n miles, 



we haveD^n-f?; w=a/-; and d may u.sually be taken 



equal to half a foot. 



Suppose, for instance, the problem — //' the eye is 1^ feet 

 above the sea level, hoio far off is the sea horizon ? 



Here we have, taking a foot as the unit of length, and 

 d=Ht. 



m=v/20-4-2=v'T0 

 = 6 J approximately 

 If we had put (^=6f inches, we should have had, taking 

 the inch as the unit of length, — 



^240 - ^ 



32 

 or « = 6i approximately. 



or 278 feet for the height of the Galley Head Light which 

 is known not to be half that height above the sea level. 



Let us see how the problem should be dealt with, taking 

 first the S inches per mile which corresponds to the 

 depression of a geometrical tangent line. 



Let LPO (Fig. 12) be the earth's surface, I the light, 

 the place of the observer's eye, IV o touching L P O at 

 L ; let L ^ be the height of the lighthouse, o the height 

 of the observer's eye above the sea, or IG ft. Then 

 PO=yl6T|=v724 = 4-9 nearly 

 .-. ?P=21— 4-9 = 16-1 miles 

 and L;=8x (161)- inches 

 = 173 feet, 

 rather less than 278 feet. 



But putting (/ =G in. we reduce the height L ^ still more 

 remarkably. For then we have 



Po = yi6 -f- if = v/32 = 5| nearly enough 

 .-. ZP = 21 — 5| = 15^ miles 

 and L/=6 X (151)^ inches 



= 1,411 inches = 117 ft. 7 in. 



Yet honest Parallax and his erudite followers quietly 

 substitute 278 feet or thereabouts as the true height of a 

 light seen 21 miles over a sea horizon by an eye 16 feet 

 above the sea level ! And one of them has just, with the 

 manners of his tribe, told Prof. Tyndall he has wilfully lied 

 in the matter. Such is the honesty of some flat-earth men ; 

 such the ignorance of others ; and such the polite suavity of 

 them all. 



Fig. 12. 



Again, suppose the problem, — If the sea horizo7i lies 20 

 miles away, how high is the eye above the sea level ? 



Here we have, taking the inch as the unit of length, 

 and (? = C inches, 



D = (20)- 6 inches 

 = 200 feet. 



If we put d = 6f inches, we get instead 

 D = 



(20)= Clinches 



= 80 X 32 inches 



= 2560 in. = 213 ft. 4 in. 



Let us next take a class of problem scarcely less simple, 

 but of more general use. 



In a letter recently addressed to the Daily News, I'rof. 

 Tyndall says that going out in the steam yacht the Princess 

 Alexandra to a distance of 21 miles from the Galley Head 

 Lighthouse, the earth's rotundity coming between them and 

 the shore, the light " dipped " beneath the horizon. Stipposing 

 the eye of the observer to have been 1 6 feet above the sea- 

 level, what is the height of the Galley Head Light above the 

 same sea surface ? 



The way in which Parallax and his followers solve the 

 problem is as follows. For 21 miles the depression of the sea 

 surface below a tangent-line is 8 in. multiplied by the 

 square of 21, or 441 — i.e. 294 feet. Hence the beacon 

 light " must have been " (here I quote one of those 

 worthies) " 294 feet above the sp.a level minus the eight or 

 ten feet of the steamer's deck." Taking 16 feet for the 

 height of the eye above the sea, this would give 294 — 16 



HOW TO GET STRONG. 



REDUCING PAT. 



WE have been asked why we have given attention so 

 fully to the question of reducing weight, as if this 

 were a point of primary importance in athletics. Our 

 reason has been that many who read (redde) our former 

 remarks complained that owing to corpulence or excessive 

 weight they found several of the suggested exercises either 

 impracticable or at least very trying and unpleasant. Un- 

 questionably nearly all exercises for increasing the strength 

 of particular muscles are much more agreeable and eflective 

 when extra fat has been removed ; and since nearly all the 

 methods available for reducing weight are good for the 

 bodily strength generally, we have thought it well to deal 

 with this really important part of our subject before passing 

 to the consideration of systematic exercise, as we shall 

 presently do. This remark as to the ell'ect of fat-reducing 

 processes applies of course with special force to the con- 

 siderations ne.\t to be dealt with, which relate to the forms 

 of exercise best suited for reducing weight. 



As a general rule it may be said that the most eflective 

 exercises for reducing the woigiit are those which act most 

 eflectively on the respiratory organs. Running for instance 

 is far more quickly eflective in this way than w-alking, 

 though quick walking is a very excellent exercise for the 

 purpose. A steady run taken every morning before break- 

 fast, and another taken every evening shortly before retiring 

 to rest will be found to produce a marked eft'ect on undue 

 deposits of adipose tissue. But here a word of caution 



