Prof. Potter on some properties of the Air Thermometer. 269 

 ing to it of the former proposition only in having the coefficient 



(1 H r \ in place of 1 . 



As the values of n and h' are not given for any experiments 

 yet published, we are not able to make calculations for compa- 

 rison with them; but can, by taking different values of the 



coefficient /lH rV see that the experiment is a dynamical 



\ 1+ w) 



one in the first instance. There is not, however, oscillation in 

 every case, as might have been foreseen ; for when a is small 

 compared with b, the adhesion is more than the active moving 

 force, and no motion ensues, the equation giving no other ad- 

 missible value for x when v = than x = a. 



For certain values of a with respect to b, and of the coeffi- 

 cient, the two values of x when v = are both positive, or A' lies 

 below as well as A. For a certain value of a and of the 

 coefficient, the second value of x for v = is x = 0; which case 

 I have calculated for the particular relation of a = 2b, which may 

 be tried when the coefficient has been determined to apply to 

 that particular case. 



When /l + -^\ =1-01, orn= '005 (l+ £), 



if a= b, then the roots are x = +a, and x= — 1*455#; 

 a = 2b, „ „ x-=- a> „ x=— l'SOoa; 



a = 3bj „ }i x= a, „ #.= — 2'065tf. 



When 



( 1+ ^) =1 ' 1,or " = ' 05 ( 1+/ ^ 



if a=z b } then the roots are x= -{-a, and x— — '994^; 

 a = 2b, „ „ x = a, „ x= — 1'400«; 



a = 3b, „ „ x=. a 3 „ x= — l'66la. 



When 



( 1+ 1 i^) =l ^ or;i=,25 ( i+ ^ 



if a— b, the roots are . . . x= +a, and x— + '26Ga; 



a = 2b, „ „ x= a, „ x=— '257a; 



a = 3b, „ „ x— a, ,, x=— '530a; 



# = 66, „ „ x= a } „ x= — '922a; 



a=9b, „ M x— a, „ x=—V270a. 



