A SYSTEM OF PARTICLES. 263 



Now the altitude of the thermometer diminishes (cceteris paribus) 

 nearly uniformly as ;• increases, hence, putting r ^ a - f, we get 



1 1 1 



e Ar + B a - bt' 



and ^ = r' (1 + ct) ; 



••• ^"-= VI {\ +ct)- 



•■■ « = KVT+Vt, 



which is the common expression. 



29. Newton's hypothesis, founded on the law of the pressure 

 varymg as _ the density, is that the particles exert on each other 

 forces varymg as the reciprocal of the distance between them, but 

 that the sphere of influence of each particle is terminated in the 

 particles immediately adjoining it. The latter clause has been over- 

 looked by many writers on the subject, although, as Professor Robisou 

 observes, it is absolutely necessary to retain it; and, indeed, it appears 

 froni our foregoing conclusion (20), that direct vibrations are incom- 



of fhe^Tstance '''"'"'^ "' '" ''''" '' '""''^ ^'^^^^"^ ^ ^^^ ^^P-cal 



There seems to have been a great disinclination manifested to the 

 adoption of Newton's Theory. Even writers, since Professor Robison 

 who have amply extracted from his work, have omitted the restriction 



tL .1 Z 1°, K r^°"""^' P'"'^'^'"^- ^'°'- '^ '* ^'^y extraordinary 

 that this should be the case, when we consider how little pretensions 

 this has to be considered a law of force at all. 



Robison mentions an hypothesis which would reduce the above to 

 a more intelligible form, which is, that the particles be supposed elas- 

 tic and in contact. At the same time he rejects it, alleging as his 

 reason for doing so, that if the particles were originally spherical, thev 

 would, before the pressure was doubled, become cubes. If this be the 

 only objection against it, I confess that it appears to me to stand on 



