601 



METEOROLOGY. 



METEOROLOGY. 



602 



spherical mass, arrived at a permanent state of temperature in each 

 part, and subject at its external surface to a given distribution of heat, 

 or to a given power of exterior conductibility. The depth at which 

 this permanence of temperature occurs is different in different lati- 

 tudes, inasmuch as the solar action on the superior stratum is also 

 different on account of the greater or less obliquity of its rays, and 

 likewise on account of the earth's elliptic annual motion. Thus we 

 have the following observed relations between the permanent tempera- 

 tures and the corresponding latitudes : 



Permanent 

 Lat. temperatures. 



Equator 0' - 78' 



Cairo 30'-2 72'-50 



Paris 48 '-50 53'-CO 



Berlin 52'-40 49'28 



Yadso ...... 70' 3l>'* 



The analytical equation for the propagation of heat in solids of any 

 form, is 



dv f cf-i- d'v d-i- 



where v represents the temperature at a point of which the rectangular 

 co-ordinates are x, y, z, and the constant K depends on the interior 

 conducting power, and t is the time. In the case of a sphere with a 

 radius B, we may place the origin of co-ordinates at the centre, and 

 transforming the above from rectangular to polar co-ordinates (namely, 

 r, the distance from the centre, 6 the angle formed by the radius vector 

 with an axis, and <p the inclination of the plane of 8 to one of the co- 

 ordinate planes, the angles necessarily disappear from the transformed 

 equation, and) it becomes 



dv td-v 2 </.-l 

 di = K ldr- + r"-rf?j' 



on the supposition that the exterior permanent temperatures were 

 uniform; to which we must annex the following equation for the 



dv 

 surface, -r + k (t 1 o) = 0, where o represents the temperature of 



the medium in contact with the globe, and h the index of exterior 

 conductibility of the globe. But in the case of the earth both K and /i 

 are variable, and the former must then be brought under the sign 

 of differentiation After there shall have been a greater number of 

 observations on the permanent interior temperatures of the earth, the 

 above equations will be very useful in enabling us to calculate the 

 temperatures at depths under the surface greater than it is probable 

 man can ever penetrate, and they will assist in the explanation of the 

 numerous phenomena which depend on the internal heat of various 

 parts of the globe, as volcanoes, thermal springs, &c. Kegarding the 

 interior parts which are sufficiently remote 'from the surface as in a 



dv 

 slate of permanent temperature, we should have -r = ; when the 



preceding equations admit of easy integration on the supposition that 

 K is constant, and of approximate solutions on a probable form of the 

 function K when variable. [HEIRIUKRATION OP THE GLOBE, and 

 TEMPERATURE, TERRESTRIAL, DISTIUBUTIOU OF.] 



With respect to the heat of the external stratum, it is principally 

 dependent on the radiation of the sun, the effect of which depends on 

 the duration and the obliquity of the solar rays, both of which are 

 dependent on the declination of the sun and the latitude of the place. 

 The integral taken throughout the year depends therefore solely on 

 the latitude : from this integral the calculated mean temperature is 

 derived, but differs in most cases from the observed inasmuch as the 

 propagation of heat in the sea and in the air affects unequally those 

 places in the same parallel which are near to or distant from the 

 coasts, and the unequal quantity of continent in the northern and 

 southern hemispheres produces a similar result with respect to them. 



The direct heat of the sun being unequally distributed over different 

 parts of the globe is the primary c nise of the variation of climate ; its 

 diurnal action on land is sensible only for a few inches in depth ; the 

 annual action however extends throughout the superior stratum of 

 variable temperature above mentioned. The mean temperature of a 

 place ia generally estimated by taking the average of the diurnal 

 temperatures during the four BKI.-OUS of the year, and again taking the 

 average of these four averages. 



An there is a great variety of temperature in the same parallel of 

 latitude, we cannot have a formula dependent only on this element to 

 express the heat of places on continents. The first approximate 

 formula to that effect which deserves the name, is that given by 

 Slayer, the celebrated astronomer ; though empirical, it is found to 

 possess considerable exactness. If t be the mean temperature in 

 degrees of Fahrenheit's thermometer, he makes t = 84 52 sin -L, 

 where L U the latitude of the place. The supposed facts which 

 evidently suggested this formula were the equatorial mean temperature 

 of 84 , which is now generally supposed to be too high; the Polar 

 mean temperature of 32", or the freezing point, which, from the recent 

 observations of Parry, Scorcsby, &c., is now known to be far too great ; 

 and thirdly, that the diminution of heat from the equator to the poles 



must proceed according to some even power of the latitude in order to 

 amount to the same quantity in equal latitudes north and south, for 

 which reason he chose the least even positive power of the sine. How- 

 ever, since the quantity of land in the northern hemisphere is about 

 three times as great as in the southern, the solar heat accumulates 

 more in the former, and in the latter is more equable between winter 

 and summer. Sir D. Brewster has substituted for Mayer's the formula 

 t = 81 50 cos L, which bears an exceedingly good comparison with 

 observations, but for the reasons above given he has found it necessary 

 to modify it for the New World. Mr. Atkinson has shown that the 

 mean of the errors of Mayer's and Brewster's formula; for ten places 

 nearly on the level of the sea are respectively + 172 and '12. 

 The temperatures of April and October are generally nearly the mean 

 of the year, which also is found to vary but little in a considerable suc- 

 cession of years. If T be the mean temperature at an altitude A in feet, 

 in a given place where ( is the temperature of the surface, to express T, 



h 



Mr. Atkinson has proposed the formula T = t - 



251 + 



JL 



200 



, giving for the 



extreme atmospheric cold the temperature 200, which is probably 

 near the truth. 



The names of Isotheral, Isocheimal, and Isothermal lines have been 

 given to lines passing through places which have equal mean summer, 

 winter, or annual temperatures, the two former having contrary courses, 

 and the third intermediate. The difference of latitude between places 

 in the New and Old Worlds, on the same isothermal line, is consider- 

 able, as appears from the following table : 



Isothermal 



line of 

 Temperature. Places. Latitude. Longitude. 



SNear Ulco, Lapland, . . 67' 20" E. 



and 

 Table Bay, Labrador . . . 54 58 \V. 



! Stockholm . . . . 60' 18' E. 



aid 

 St. George's Bay, Newfoundland 48" 49 W. 



iBelsium . " . . . . 51' 2 E. 



and 

 Boston, U. S 424 71 W. 



! Near Home . . 43' 113 - 



i.nd 

 Kaleigh, N. Carolina . . 36 76j' W. 



or we may average according to latitude thus : 



Mean Temperature of Mean Temperature of 



Latitude. West of uld world. East of New World. 



30' 70-52 60-92 



40 U3-14 51-50 



50 50-00 37-94 



60 40-64 23-72 



The mean temperature in the latitude of 34 in different continents, 

 and at places near the sea, is found to vary but little, thus : 



Places. Continents. Latitudes. Temperature. 



Cape of Good Hope . . Africa 33 51' 6G'-7 



I'ort Jackson, N. Holland . Australia 33' 53' CG'-D 



City of Bucuos Ayrcs . . America S4 1 30' 67-5 



The sea varies in temperature much less than the air ; the region 1 of 

 warmest water extends about 5J on each side of the equator, but 

 rather farther to the south than to the north. There are two points of 

 maximum cold near the North Pole ; one of 3^ Fahr. in the neigh- 

 bourhood of Melville Island, and another of 2 Fahr. somewhere about 

 the 79th degree of north lat., long. 120 east. The isothermal curves, 

 " accordingly, about the North Pole bear no inapt resemblance,' as 

 remarked by Sir David Brewster, " to the isochromatic lines, or 

 coloured sphicro-lemniscates exhibited by polarised light in a biaxal 

 crystal, whose optic axes are inclined to each other about 30, having 

 the pole itself almost centrally situated between them, and their line 

 of junction nearly coincident with that diameter of the polar basin 

 which intersects it, and passes through its two great outlets into the 

 Pacific and Atlantic oceans a most remarkable feature, strongly indi- 

 cative of the absence of land, and of the prevalence of a materially 

 milder temperature (possibly not averaging below 15 Fahr.) at the 

 actual pole. Of the point or points of maximum cold in the southern 

 hemisphere we know nothing." An unexpected and most interesting 

 consequence has followed from Sir D. Brewster's recognition of the 

 resemblance of the north polar isothermal curves to the isochromatic 

 lines of polarised light in the case described. Sir John F. W. Herschel 

 has found that there is a coincidence between the two sets of curves, 

 " in respect of the arithmetical progression of temperature in the one 

 series corresponding to that of chromat.c sequence in the other," which 

 he points out " as something different from and additional to a mere 

 general resemblance of form ; " though " it will of course be under- 

 stood," as he observes, " that we have not the slightest intention of 

 tracing any fhyriml analog;/" between them. What the relation can 

 be, of which this coincidence is a result, it is impossible to say ; but it 



