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XXXIII. Jn improved Demonstration that Air expands in 

 Geometrical Progression for equal Increments of Heat. J^y 

 Mr. H. Meikle*. 



A CONSIDERABLE time has elapsed since I tirst pointea 

 ^o?t the n.istake+ into which MM^ de L ^a- -d Po.s^^ 

 son had fallen, in attempting to n.vest>gate the tiue^ca^^ 

 the air-thermometert. Whoever attends to the subject will 

 have little difficulty in perceiving that these great matheraa 

 ticLns misled thenLlvL by affecting to t,-eat the q-^^^^^^^^^^^^ 

 profoundly, and by unnecessariv employing some of the more 

 indeterminate branches of the differential calculus They no 

 doubt set out with data amply sufficient ff their purpose 

 but after proceeding so far, they contented themselves wth 

 the humble shift of ° s«.;«»/.^ that the ^°^7" "^^^^^f^e" 

 duatin- the air-thermometer forms a true scale of tempei ature. 

 Thai they should have failed to prove such a scale to be a 

 true one, need excite no surprise; for we shall soon see that 

 "s utte ly incompatible with the very principles from which 

 tl y atten^ted to'deduce it. It will also be seen that -d 

 these philosophers used a much more simple mode of reason- 

 n'somewhrt of the geometrical form, and aided by a diagram 

 orlwo tley might have arrived at the only legitimate resul 

 o wh'ch the da^ta will allow. But it is too well k"o;" t^iat 

 a French mathematician would much rather run the risk ot 

 losing himself than employ any such means. .-fl. ,_tial 



While many discoveries are attributable to the 'hfiential 

 calculus and the theory of functions, it is to be regretted hat, 

 of late, the unnecessary and incautious employment o then 

 more Abstruse branched for almost every purpose has tended 

 crreatly to obscure science, to retard its progress, and to sane 

 tion errors -.—this, the subject before us will illustrate. 



My object at present is (o show in a still more elementary 

 way than I have yet done, that, without the aid of any assump- 

 1:1% very d^ata used by the French philosophers, when 

 nroperlv managed, necessarily lead to the conclusion, that, 

 Sra^onsta^t pressure, tl/e expansions o" contractions of 

 air form a geometrical progression, whilst the n.crejit^^^^^^^^ 

 decrements in its quantity of heat are umtorm. But piepa 

 ratory to this, I must premise the following 



* Communicated by the Author. a„„.,1c nP Phil for No- 



t Edin. Phil. Journ. for July-September 1 ^26 ; Anna s of Ph. .. J, INo 

 vember 1826rand afterwards more particularly, Quart. Jouru. ot science 



%'SS^'S^.i'S.. V. p. 127 ; Annates ^ CMmi. for August 1823. 

 p. 337 ; Phil. Mag. for November 1^H23. ^^^^^^^^^ 



