10 Professor Hamitton’s Third Supplement 
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by means of the two first of which, combined with the relation already mentioned, 
namely, 
0=Q (6, 7 v, x) (K’) 
which depends on, and characterises, the nature of the final uniform medium, we can 
eliminate o, 7, v, from the equation (D’), and so deduce V’ from VY. 
In like manner, if both the extreme media be variable, then the seven quantities 
otvo rv x may in general vary independently, and the equation (C’) resolves itself 
into the seven following, 
oT oT oT éT eV 8T OL, MO : ; 
3 =O 5, SU lig, Pig = ig age aemepiy rlesetaey ieh 2 (L) 
by the three first and three last of which we can eliminate or v o'r’ v' from (F"), and 
so deduce /” from 7. And in the same case, or even in the case when only the 
initial medium is variable, the three last of the equations (L’) are true, and suffice to 
eliminate o', 7’, v', from (H’), and so to deduce VY from T. 
But if the final medium be uniform, the initial being still variable, then o, 7, v, x; 
are connected’ by the relation (A), while o'r’ v’ remain independent ; and instead of 
the four first equations (L’) we have the three following, 
a7 ae = a a tay 87 
Se ae” ay ay ; 
Besa = wean = Serhan 7 ener” atop) 
ie oF SS ax 
by the two first of which, combined with the relation (’), and with the three 
last equations (Z’), we can eliminate o, 7, v, ¢, 7, v, from (F"), and so deduce /7 
from 7. 
If both the extreme media be uniform, we have then not only the relation (A‘’) for 
the final medium, but also an analogous relation 
0=Q' (o, T Vy x) (N’) 
for the initial ; and instead of the seven equations (L’), we have the two first of the 
equations (J/’), and the two following, 
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