Resistance of Fluids. 401 



On the supposition that c = a, or, in other words, that the 

 velocity of the sail is equal to that of the wind, we have 



tang x = 



Assuming as an approximation, in order to find x from this 

 equation, that its value is 54 44', we obtain as a nearer approxi- 

 mation x = 65 24'. Taking the sine of this angle, and substi. 

 luting it as an approximation in the second number of the equa- 

 tion, we find, as a still more correct approximation, x = 68 54'. 

 Substituting this again for a?, we find, as a fourth approximation, 

 x = 69 4', which we consider as the correct value. 



Let us again suppose that c = 2 a, or that the velocity of the 

 sail is double the velocity of the wind, then the formula becomes 



tang* = (2+ (3 v-i 

 \ \ dn 



3 



sin 



Substituting 75 as the value of a?, we obtain as a first ap- 

 proximation x = 77 3'. Substituting again this value, we 

 deduce as a second approximation x = 77 7', which may be 

 considered as the true value of x in this case. 



The theory of winds has not arrived at that degree of per- 

 fection which renders science subservient to the purposes of life. 

 We can as yet only attribute them in a vague manner to the 

 operation of a few general causes. From what we know of 

 the expansibility of air by heat, one may easily conceive how 

 the atmosphere must always be in a state of commotion, some 

 parts of it being exposed to an intense temperature, while other 

 are comparatively cold. The portion which encircles the torrid 

 zone, by receiving the rays of a vertical sun, is much rarer than 

 that which surrounds the higher latitudes. Hence, in order to 

 maintain a due equilibrium, the aerial column at the equator 

 must be higher than it is in colder climates. This was found to 

 be the case by Mr. Casson, who observed that for the same ele- 

 vation, the barometer falls only about half as much in the torrid 

 as it does in the temperate zones. 



Mech. 51 



