( 194 ) 



§ 11. Representation of the observations by a formula. 



a. It was obvious that the formula of Avenarius: 



t f t 



100 ^ V1Ö0 



can give a siifücient agreement for a very limited range only. If, 

 for instance, the parabola is drawn through 0°, — 140° and — 253°, 

 we find: 



a= + 4.7448 



6= + 0.76117. 

 In this case the deviation at — 204"^ amounts to no less than 7°. 

 If we confine ourselves to a smaller range and draw the parabola 

 through 0°, —88° and —J 83°, we find: 



a— i- 4.4501 



ft = + 0.57008, 



while at — 140° the deviation still amounts to 1°.3. 



Such a representation is therefore entirely unsatisfactory. 



b. With a cubic formula of the form 



100 ^ \iooJ ^ vioo 



we can naturally attain a better agreement. If, for instance, we 

 draw this cubic parabola through 0°, —88°, —159° and —253", 



we find : 



a=z + 4.2069 



6= + 0.158 



c= — 0.1544 

 and the deviation at — 204° is 0°.94. A cubic formula confined to 

 the range from 0° to —183°, gave at —148° a deviation of 0°. 34. ^) 

 A cubic formula for i, expressed in E (comp. § 2), gives much larger 

 deviations. ^) 



c. A formula, proposed by Stansfield ^) for temperatures above 

 0°, of the form 



1) As we are going to press we become acquainted with the observations of 

 Hunter (Journ. of phys. chem. Vol. 10, p. 319, 1906) wlio supposes that, by 

 means of a quadratic formula determined by the points — 79^ and — 183°, he can 

 determine temperatures at — 122° to within C^.l. How this result can be' made 

 to agree with ours remains as yet unexplained. 



2) After the publication of tbe original Dutch paper we have taken to hand 

 the calculation after the method exposed in § 12 of a formula of the following form: 



E = a-^ 4- h I — I + c ( -^ 1 4- e ( -~ 



100 ^ viooy ^ Vi^v ^ vi^o 



We hope to give the results at the next meeting. 



3) Phil. Mag. Ser. 5, Vol. 46, p. 73, 1898. 



