164 TABLES OF DIFFERENCES OF MEAN TEMPERATURES. 



The progression of the tabular numbers from hour to hour is quite regular, particu- 

 larly for Mohawk. The amount of variation is nearly the same at Toronto and 

 Mohawk, but less at Philadelphia and Sitka. In general the variability in winter 

 is more than double that of summer; this latter variation will be found further 

 investigated under the head of the annual fluctuation. 



In winter the maximum variability at any hour is to the minimum variability as 

 5 to 4, and in summer as 8 to 5. 



Multiplying the above average probable errors ^ 2°. 8 in winter, and ^ 1°.2 in 

 summer by y' 30.4 or by 5.5 nearly, we have an approximation to the probable 

 error of an observed temperature at any hour of the day at these seasons, with 

 reference to the normal values of that hour, month, and season. These quantities 

 are ^^ 15° and J:; 7° respectively. 



Any attempt to deduce, for any given time and place at the earth's surface, even 

 approximately, the daily fluctuation of the temperature, as far as it depends upon 

 the variations of the sun's altitude^ and with consideration of the loss of heat by 

 absorption while passing through various depths of atmosphere,^ must lead to 



' Let ? = the sun's zenith distance, S its declination, t the hour angle, then for the latitude ^ 

 cos f = sin t sin S -|- cos f cos 6 cos t, 

 from which expression the altitude or depression of the sun for any hour of the day may be computed. 



^ If we treat the length of the oblique path of a ray of heat passing through the atmosphere simply 

 as a geometrical problem, it is given by 



l = \/ r'' cos^ f -)- 2r/i -\-h^ — r cos if, 

 hence for the case of a horizontal ray (irrespective of refraction), 



L = V 2rh + h% 

 where r = the earth's radius and h = the height of the atmosphere. Taking for instance h = 45 st. 

 miles, at which elevation twilight yet indicates the presence of air capable of reflection, and r = 3956 

 miles, we find that horizontal ray must traverse nearly 600 miles of atmosphere or 13.3 times the 

 vertical thickness, if h = li miles, which is the average height at which shooting stars become in- 

 candescent when coming in contact with the atmosphere, the length of path is about tTO miles or 10.4 

 times the vertical thickness. The decrease of heat of inclined rays is greater than that resulting from 

 the inverse proportion of the length of tract, and is due to the density of the air increasing geometrically, 

 while the depth increases arithmetically. The following measures of atmospheric tract and of calorific 

 effect on a surface vertically exposed to the ray, is extracted from a table given in the Encyclopasdia 

 Britannica (8th edition), article, climate ; it supposes that of one thousand rays, vertically incident on 

 the outer boundary of the atmosphere, only 750 will be transmitted through it and received on the 

 ground. The numbers in the column headed "H" are computed by the formula (f) ' given in 

 the article meteorology, according to which only 667 rays reach the ground. The last two columns 

 contain the number of rays incident on a horizontal surface, obtained by multiplying the numbers in 

 the preceding columns by cos f. 



Zenith 



Length of 



Rays 









distance. 



atmospheric 



transmitted. 



(..jsecj; 



L cos { 



jycos? 



i 



tract. 



(^) 



(^) 







o° 



1. 000 



750 



667 



750 



667 



10 



1. 015 



747 



663 



735 



653 



20 



1.064 



736 



650 



691 



611 



30 



1. 154 



718 



626 



619 



542 



40 



1-305 



6S7 



589 



526 



451 



SO 



1-554 



640 



531 



411 



341 



60 



•-995 



563 



444 



282 



222 



70 



2,90s 



434 



306 



148 



105 





5.610 



199 



97 



35 



17 



90 



37.850 



















