392 Astronomical and Nautical Collections. 



acknowledged sufficiency of the French table, with which it 

 agrees, in all ordinary cases, and upon its coincidence with the 

 mean of 156 observations of Mr. Pond in low altitudes, as well 

 as with Bradley's empirical correction for temperature near the 

 horizon. 



Nor would it be necessary to inquire whether or no the series 

 is capable of being employed with convenience for an atmo- 

 sphere of uniform temperature, in order that it may be "whispered 

 into a pit" that an unjust judge has been metamorphosed. But 

 the thing is really so easy, in comparison with other modes of 

 computation, that it is not fair to the question to omit a further 

 exemplification of the method proposed, with the assistance of 

 the subdivision of the operation into two parts, which has been 

 already suggested: and the whole may be resumed with little 

 difficulty, from the first elements of the problem. We shall 

 have, therefore, 



X, the distance from the centre, 



y, the superincumbent weight, 



z, the density, here represented by y, 



dy =: — mydx ; -I.-=i — mdx ; hly — m — mx. 



y 



M, the perpendicular to the direction, 

 $=:?(", the initial value of m, 



o c 



; — p&y 



