104 Introduction to the Seventh Section 



the temperature of freezing water to be = 60"*303, it is at the 

 temperature of x degrees of the centesimal scale. 



1. For perfectly dry air, 



60"-303 



— 1 + x. C60375 " 



2. For air saturated with vapour, 



60" -224 -f z. 11 "-629 



— 1+ x. 0-00375 _ ' 



where according to Laplace log. Br. z= — 0-0154547(100 — .r) 

 — 0-0000625826 (100— x) 2 . 



These two hypotheses give therefore for temperatures which 

 usually take place at Kbnigsberg, the value of the constant 

 quantity / Hyp y H „ 



— 10° 62"-653 62"-624 



60 '303 60 -303 



+ 10 58-123 58-189 



+ 20 56-096 56-271 



+ 30 54-205 54-563 



from which it is evident that refraction undergoes less 

 change by the second than by the first hypothesis : the num- 

 bers for the former might be nearly represented by the for- 



. 6Q"-33Q 

 mula i + x. 0003566* 



In order to preserve the common form of computation, the 

 tables ought, therefore, to be founded on this formula, if that 

 hypothesis were the correct one. Without measuring, there- 

 fore, the actually existing quantity of vapour which is not jet 

 introduced in observatories, a nearer approximation to truth 

 may be obtained by adopting for the change a formula in which 

 the constant number is between 0*003566 and 0-00375, than 

 by using the latter number : the formula for the change which 

 ought to be used, depends on the mean ratio of the vapour 

 contained in the atmosphere, to that which is required for sa- 

 turation ; and as there are no direct satisfactory observations 

 on this subject, it may most safely be derived from astrono- 

 mical observations. 



If we represent the mean refraction as contained in the 

 table of the Fundamenta Astronomice by g, the state of die ba- 

 rometer and the interior and exterior thermometer by b. t', t 

 (Paris lines, centesimal degrees, Fahrenheit's degrees), the 

 refraction by which the observations have been reduced, is 

 calculated by the formula 

 , { b j + io. 000018484 )Ap- l0 ^o-oo20779 ^x 



£ ~" ^ I 33328 ' 1 + t' 0-00018484 * < '+(*— 50) 0-0020779 S • 



If, 



