6 On the Constitution of Matter, 



It must be observed that this is little, if anything, more than a 

 statement in a mathematical form of some of the most obvious 

 properties of ordinary matter. It remains to be seen whether 

 this statement or assumption is consistent with, and can explain 

 other and more recondite properties. 



In order to satisfy approximately the condition thaty (/3) must 

 be very small, I have made it zero, giving to f[x) = 0, three 

 roots equal to /3. Any odd number of roots would apparently do 

 as well as 3, but there are good reasons for believing, as I shall 

 shew hereafter, that 3 is the correct index. 



The equation of motion is 



which may be solved approximately when z is small compared 

 with h. Neglecting the last term the equation may be written — 



d-z 2 3 m- ( „ s?\ 



When t = 0\&i z = a, ~ — 0, where - is small. For a first 

 dt h 



approximation we have 



z =■ a cos mt. 

 By the usual method of successive approximations, z may be 



developed in terms of -. The process requires some care, but 

 h 



involves no particular difficulty, so that it will be sufficient to 



give the result, which, to the degree of approximation required 



for the present purpose, is 



z = a {_A coscmt + B p + G co%2cmt + I) p"- co&Zcmt'] 



where 



p = 



a 

 li 













A = 



- 1 



- p + 



55/ 

 32 









B = 



3 

 2 



(1- 



2p + 



147;?' 

 16 



) 





C = 



- 



i(- 



- 2p) 









D = 



9 



32 













c^ = 



1 



21^ 

 4 



2 







c being a factor nearly equal to unity, which, as in the Lunar 

 Theory, it is necessary to introduce. In conducting the 



