584 Mr. R. Garrrtichael on the Singularities of Physical Science j 



this illustration at some length, as it is suggestive of some points 

 most valuable in a theoretical point of view. 



At first sight it would seem as if a knowledge of the con- 

 ditions which have been just stated would be sufficient to deter- 

 mine the law of expansion, the method employed being appli- 

 cable to all similar cases. 



Thus ht being the coefficient of expansion, supposing gene- 

 rally that . I -u J jj >Lti ijv 

 .idvU\vft\\\m\ \ S^stf{t)y<(*m If^di rTwon>l fbw gi iJ 



it is evident that the form of /must be discontinuous ;' *ih^ nrst 



break occurring for t = 75°, and a second at the valiie Hf % 6ot^ 



responding to the point of vaporization.'*^ >^-.o.ro,„rm.o /bod adj 



Moreover for ^=55°, we should have^^^'* '^M "^^f ^'^''" '^^^ 



for /— 35 , ,,,,«^, •LMuh^aoTq sfU rftod moil 



, ,.a.. . /(35)=0, /'(35) <6;,, ,^|,,,,,j ,,,^ ^| 



anil sino^ llh«^to|ume at 75° is equal to the voi^itfit&iAt "86^* ^olq 

 ,013^ biifov/ tl^ .89^j8.t« y!'75') =s /TSil ^^"^^^ '^'^■'^ ^sslufuioi fsaif 



These conditions, however, are manifestly insufficient to det^^« 

 mine the form of /, or the law of expansion of the metal ; indeed 

 it is evident that an infinite number of curves might be described 

 so as to satisfy those cofj^iti^ps^.jjjjt jfhat;,,fige,9^^^ ^fiix^ffi 

 give the law required. ,,^,.,^.,,.,,-. i^,,,.,„f; .,,,.^.,, u ^,, .^^^^.^ 



This remark will serve to explain a difficulty alluded to by 



M. Pierre* with regard to the expansion of liquids. ; He ha^ 



shown, that, although the formula terfi nwodn 8«ii Hoia msbom 



8^=at + bt^-\-ct^ V$^o^ 



in general repres6nts their expansion with considerable acic?utoy, 

 in some cases we must adopt different coefficients for the upper 

 and lower parts of the thermometric scale. Thus in the case of 

 amylic alcohol, or fusel oil, the coefficients for temperatur^fe 

 from —15° to +80° Cent, differ from those suited to the rangidi 

 from 80° to 131°. M. Pierre states also that a formula of this 

 kind fails to represent the expansion of water between the limits 

 — 13°*14 and 100°, and that he has not succeeded in discovering 

 any simple expression which will do so. 



From what has been said it is obvious that a priori this 

 should be so, unless the formula express the exact law of expan- 

 sion, which is by hypothesis unknoiun. The partial coincidence of 

 the deductions from the formula with the results of experiment 

 is easily intelligible from the circumstance, that any two curves 

 possessing tolerable regularity and passing through the same 



il >!3£II03 



* Annates de Chimie et de Physique., vol. xix. p. 210, 3x,^^^e^^y ^^ 



