Prof. Bartlett on the Comas and Tails of Comets. 63 
to some other, founded in better ascertained laws of matter. The 
question is not one of pure mathematics, but of physics. 
d?x d?y d2z d 
sal (3 -x)pe4(53 _ v)ov+(5 471)d2|=0 : 
in which m is the mass of an element, 2yz its codrdinates of 
place, X YZ the sums of the components of impressed accelera- 
tions in the direction of the axes «yz, respectively. 
The conditions of aggregation may be expressed in some func- 
tions of the codrdinates of molecular places. As three codrdi- 
nates determine the place of a single molecule, there will be three 
times as many codrdinates as molecules; and if « be the number 
of molecules and 4 the number of equations that give the condi- 
tions of aggregation, then will 8«—4=n be the number of coér- 
Fut, n't’, &., be the increments of «fy, a’ 67’, &c., at any in- 
stant and due to any transmitted initial disturbance, it is easily 
shown that 
. = R.N,.sin (t.»/o —7), 
7 = > R.N,.sin (t.4/@—7), © 
¢ = SR.N,.sin (t.-/e—7); 
. &— &e. &e. &e. 
In which there are n terms comprehended by the sign 2, and in 
Which ¢ will, in general, have different values from one term to 
another. When these values of ¢ are real and positive, the dif 
t terms in the values of § 7, &c., will disappear periodically, 
the precise times of disappearance being given by 
t.a/@ —r—a7; tr/o—r'=a'a; ke., ke. 
1 f 
io eas =o A : tao oe ; &e., &e. 
Ich a@ is an . The intervals of disappear- 
ance will be y whole number. ppe 
or 
eer Me. ee 
i. Mt we “acing : 
if these intervals be commensurable, all the terms will dis- 
