182 



KNOWLEDGE. 



Mav. 1911. 



38. THE EFFECT OF GR1:AT ALTFIUDES ON 

 THF..ARS. — Is it true that persons ascending mountains 

 experience, on reaching great altitudes, bleeding of the ears ? 



If so, would not this bleeding be beneficial to persons 

 suffering from any congestion of the ears ■ 



Thirdly, could an atmospheric condition similar to that 

 which obtains at great altitudes be produced on the sea-level 

 by any scientific process ? p t, 



i9. ANTI-CVCLONE.— I should be much obliged by your 

 favouring me with an explanation of the term " .Anti-Cyclone." 

 I have always understood it meant the opposite of Cyclone, 

 viz., a perfect calm. This I have had disputed, and that the 

 storms we have lately had from the Easterly have been caused 

 by an '" .\nti-Cyclone." Now, if .Anti-Cyclone and Cyclone 

 both mean storms. w-h\- the prefix ".Anti"? Some of the 

 books I have, merely, give "Cyclone," but do not mention 

 " Anti-Cyclone." or if the term is referred to, it is only in a 

 very \'ague wa\', and the language is by no means plain or 



e^P'''"'^*'"'-^'- Wm. S. Jeffery, 



40. WATER-FINDING.— The other day. Mr. Pogson, a 

 well-known water-diviner of Madras, located as many as six 

 subterranean springs in a garden in Cuddalore, India, Wells 

 were sunk at all the six spots, and. strangely enough, water 

 was found in all of them at very nearly the same depth, and 

 in approximately the quantity calculated by the diviner. 



Like all other water-finders, Mr. Pogson locates water by 

 means of an ordinary rod — either of wood or of metal — 

 which, without any volitional effort on his part, spontaneously 

 rotates in his hand when he stands above a bed of water 

 underground, or points vertically downward if he happens to 

 be over a spring of small dimensions, I should be very 

 much obliged if a scientific explanation can be gi\en of this 

 wonderful phenomenon. 



It mav be well here to point out that Mr. Pogson is also 

 endowed with magnetic susceptibility, by which he can tell 

 wliich pole of a bar magnet is turned to him. Hallcy's comet, 

 he sa\-s, affected him before and after its perihelion passage, 

 exactly like the North and South poles of a magnet. 



T. K. Joseph. 



REPLIES. 



10. WATER AND ITS OWN LEVEL.— The real mean- 

 ing of the common expression that water finds its own level is 

 identical with that of Mr. Yerward James (" Knowledge," 

 March. IQll, page 103) that it seeks its " Appropriate Spherical 

 Cur\ature." What he says about the variation in the surface 

 of a cup of tea when lifted may be true, but there are so many 

 influences in operation that it might take a little time for the 

 fluid to adjust itself, the motion of lifting having some action 

 besides the effects due to inertia, capillarity and friction. So 

 the centre of gravity of the earth is affected by any displace- 

 ment of particles on the surface of the earth, such, for instance, 

 as when a boy throws a stone, or when a crane lifts a mass of 

 rock, or when a ship takes a cargo of coal from one place to 

 another. 



As regards experimental proof of the convexity of the surface 

 of water, reference should be made to the experiment tried on 

 the Bedford Level Canal, a straight piece of water six miles 

 long. This e.xperiment w-as fully reported in The Field 

 newspaper, March and .April, 1870, and might be considered 

 proof conclusive of the con\exity of the surface of water. 



Lumen Marti.wum. 



30. FINDING THE TIME, BY DAY.— (11 Local apparent 

 time can be roughly found when the ratio of the length of an 

 upright stick to the length of its shadow is known, by using 

 the following method : — 



Taking the data given by " Interested," and the angles to 

 the nearest degree of arc, we have latitude = 52° and Sun's 

 declination on the given day=15' North. Call the length of 

 the stick unity: then in the right-angled triangle whose 

 perpendicular and base is the length of the stick and shadow 

 respectively, we must find the angle .ABC. In the given case 

 (shadowtwice the length of thestickl tan "' J =27" = angle CAB 



which is the altitude of the Sun above the horizon at the time 

 the measurements are taken. It will now be necessary to find 

 the uorthmost angle of a spherical triangle on the celestial 

 sphere, three sides of it being given, viz. (90° — Sun's altitude) 

 or Sun's zenith distance, the Sun's angular distance from the 

 north pole of the heavens, and the colatitude of the place. 

 Using the formula 



' — 'cos s, sin (s — a) 



sin ^-y ^ 



cos 1. sin p, 



where P is the angle required (being the Sun's angular distance 

 from the meridi.an and therefore equal to the time), a the 

 altitude of the Sun, / the latitude of the place, p the Sun's 

 polar distance, and s half the sum of the three last mentioned 

 quantities, the times deduced are either 7'' 44™ a.m. or 4'' lb"" 

 p.m., the shadow in this particular case having the same 

 length twice during the day. This process, by the way, is 



2e.,vtf^ 



pie. n V 



similar to that used to find time at sea except that .i sextant is 

 used to measure the altitude of the Sun instead of the ratio of 

 the length of a stick to its shadow. 



(2) In the latitude of London the length of a perpendicular 

 stick is equal to the length of its shadow at noon at about 9th 

 April and 5th September of each year. The reason is 

 apparent from a study of the figure. With the sun on the 

 meridian and with the stick and its shadow of equal lengths we 

 have, by elementary geometry, the angle .ABC = 45', which 

 must be the altitude of the Sun at noon. Now the colatitude 

 of London is about 38 (see Figure D so that the Sun will 

 require to have a northerly declination of 7' to make its 

 meridian altitude = 45 and the Sun's declination has such a 

 value on the dates mentioned. 



(3) The latitude of any place can be found, if the ratio of 

 the length of the stick to its shadow at noon is known (the 

 Sun's declination being also known approximately), for by the 

 first answer the altitude of the Sun can be found from the 

 given data, and by the figure it is seen that the latitude when 

 the Sun is north of the celestial equator is equal to its zenith 

 distance {i.e.. its altitude subtracted from 90^) added to the 

 northerly declination, and when south, the latitude is equal to 

 the Sun's zenith distance minus the southerly declination. 



Xote. — In the figure the length of the stick is drawn out of 

 all proportion to the other lines. The stick, if drawn to scale, 

 would require to be represented by an infinitesimal line on an 

 infinitely small earth situated at the centre of the celestial 

 sphere, half of which is shown. ^^^^_ ^ ^^^^^^_ 



30. To find the time of the day by comparing tlie ratio 

 between the length of a stick and that of its shadow involves 

 the solution of a spherical triangle. 



The fornmla for determining the hour angle is as follows: — 

 sin — = A^/ f cos H0 + -^ + °) sin i (0 -f A - "^ \ 

 ^ ^ \ cos <p sin A ) 



where is the latitude, A the polar distance of the Sun. or 

 90 - declination, a the altitude, and /; the hour angle. 



