138 Prof. Thomson on the (Economy of the 



modified Bezoutian form of (78)^ the assumption 



will, the functions e being determinable, suffice for the evanes- 

 cence of Yj*. 



4 Puni]} Court, Temple, 

 December 27, 1853. 



XX. On the (Economy of the Heating or Cooling of Buildings 

 by means of Currents of Air. By Professor W. Thomson f- 



IF it be required to introduce a certain quantity of air at a 

 stated temperature higher than that of the atmosphere into 

 a building, it might at first sight appear that the utmost oeconomy 

 would be attained if all the heat produced by the combustion of 

 the coals used were communicated to the air ; and in fact the 

 greatest oeconomy that has yet been aimed at in heating air or 

 any other substance, for any purpose whatever, has had this for 

 its limit. If an engine be employed to pump in air for heating 

 and ventilating a building (as is done in Queen^s College, Bel- 

 fast), all thewaste heat of the engine, alongwith the heat of the fire 

 not used in the engine, may be applied by suitable arrangements 

 to warm the entering current of air ; and even the heat actually 

 converted into mechanical effect by the engine, wiU be recon- 

 verted into heat by the friction of the air in the passages, since 

 the overcoming of resistance depending on this friction is the 

 sole work done by the engine. It appears, therefore, that 

 whether the engine be oeconomical as a converter of heat into 

 mechanical work or not, there would be perfect oeconomy of the 

 heat of the fire if all the heat escaping in any way from the engine, 

 as well as all the residue from the fire, were applied to heating 

 the air pumped in, and if none of this heat were allowed to 



* It will be seen, from my investigation at pp. 45, 46 of the Supjile- 

 mentai-y Number to vol. iii. of the Mathematician, that the equation 



a^ + a3r + bx-\- — =0 

 3a 



admits of finite algebraic solution. I have discussed another solvable form 

 of quintic at pp. /'>< 77 of the ' Diarj' ' for 1851 . Euler has devoted §§ 44, 

 45, and 4() of his paper De resobitione, &c. to the consideration of another 

 solvable form. Bczout has jiointed out others (Par. Mem. for 1765, p. 644). 

 t Communicated by the author, having been read before the Glasgow 

 Philosophical Society, November 15, 1852. Mathematical demonstrations 

 of the results stated in this jiaper are jniblished in the form of the solution 

 of a problem in the Cambridge and Dublin Mathematical Journal, Novem- 

 ber 1853. 



