Account of certain Improvements in Involution and E volution.34 
instance, are the sudden stopping and gushing out of fountains, 
occasioned by the opering or contracting of fissures ; the dizzi- 
ness and sickness people feel, from the almost imperceptible wave- 
like motion, &c. 
107. Secondéy, Those appearances which seemed to depend 
upon particular circumstances, and of which therefore, unless we 
had a more exact knowledge of the countries where they hap- 
pened, it would have been impossible to give any account, with- 
out having recourse to uncertain conjectures: of this kind was. 
the greater agitation of the waters in the lakes of Switzerland, 
at the time of the earthquake of the Ist of November 1753, than 
during the earthquake of the 9th of December following*, though 
the houses upon the borders of them were more violently shaken» 
by the latter. And, 
108. Lastly, Those appearances, which only seem to have an 
accidental connection with earthquakes, or the causes of them; of 
this kind, are the effects which, in some instances perhaps, they” 
produce on the weather; the distempers which are sometimes 
said to succeed them; the disturbance which, we are told, they 
have sometimes occasioned, during the shocks, in the direction of 
the magnetic needle, &c. none of which are observed to be con- 
stant attendants on earthquakes, nor do they seem materially te 
affect the solution given either one way or other. 
LY. Account of certain Improvements in Involution and Evolu- 
“tion. By Mr. Prrer NicHoLson, 
INVOLUTION. 
I HAVE not observed in any of our treatises on Algebra, any 
general form for the expansion of (a+b+ce+d+e+ &c.)” ,ex- 
cept that which would result from the theorem of Demoivre: 
but as this is capable of a more simple form, which does not in- 
volve the combinations of the quantities, and on which the ex- 
traction of roots in numbers entirely depends, I shall here ex- 
hibit it thus: 
(at+b+c+d+e+4&c,.)" = an 
nu—l in—Il.n—2 
(2), f- ; nar—l [) 4 3 Qn—2 [24 ew + 
n.n.— 1.n—2.n—3 } 
FoumneK f chin tah bs + &e. } 
(3),+ } n(a+b)"—e4 aim (a+ byrPer pM at Lire 
+ &c, ; 
* See Monsieur Bertrand’s Memoires sur les Tremblemens de Terre. 
Y3 (4), 
