Mr. J. K. Laughton on the Permanent and Periodic Winds. 443 



version should be effected would either conduct us to the expres- 

 sion of the roots of algebraic trinomials by means of indefinite 

 integrals, or enable us to see why attempts to obtain snch inte- 

 grals fail when we pass the fourth degree*. 



" Oakwal " near Brisbane, Queensland, 

 Australia, September 19, 1867. 



LVIII. On the Natural Forces that produce the Permanent and 

 Periodic Winds. By J. Knox Laughton, B,A., R.N.f 



AS we examine further into the ordinarily received explana- 

 tion of the trade-winds, we meet the distinct enunciation 

 of the hypothesis that when air is expanded by heat, so that its 

 volume is increased and its density diminished, colder and denser 

 air will force itself in, and that with velocity enough to make a 

 sensible current. This hypothesis is so thoroughly in accordance 

 with our knowledge of the properties of fluids, with our daily 

 experience, and with the principles on which coal-mines are suc- 

 cessfully ventilated, that we accept it readily, and feel no doubt 

 that colder air will force its way into the place occupied by the 

 warmer, whether with a sensible velocity or not, if some stronger 

 cause does not prevent it. But as a matter of fact, and especi- 

 ally in the phenomenon of the trade-winds, the air does not 

 stream in towards the place of greatest heat. The temperature 

 of the air over the sea on or near the equator, according to very 

 numerous observations, is seldom much in excess of 82° F. ; and 

 at sea the decrease as we approach the poles is tolerably regular. 

 On shore the case is widely different. The hottest parts of the 

 world are in extratropical countries, where during the summer 

 season the thermometer rises very far above 82°. During the 

 summer months, the temperature over a large part of Africa to 

 the north of the tropic, according to the observations of Dr. 

 Barth, is seldom less than 90°, whilst it often rises to consider- 

 ably more than 100° ; 112° is not unfrequent ; and other travel- 

 lers have noted much higher numbers. A similar degree of heat 

 is found in Arabia and Persia. Humboldt gives 93 0, 2 F. as the 



* Meditations of the night upon the developments indicated in the text 

 have led me to the opinion that the definite integrals of the resolvents for 

 the first four degrees inclusive will be convertible by a uniform process, 

 that (unless there be some modification of this process) the conversion of 

 those for the fifth and sixth degrees will depend upon the solution of a 

 linear differential equation of the second order, and that the conversion 

 of those for the seventh, eighth, and other higher degrees will depend 

 upon the solution of linear differential equations of the third and other 

 higher orders. — Brisbane, September 20, 1867. 



t Communicated by the Author. 



2 G2 



