Since dp4+(-)P+T1(p +q qi 1)!dd4, the solutions of the partial differential equation d P4 =o are the single bipart forms, omitting s P4, and we have seen that the solutions of p4 = o are those monomial functions in which the part pq is absent.
They may be regarded as obtained from a series Po + (Qi - Qo) + (Q2 (P2 - 1:11) +..
For if C l and C2 are the capacities and Q i and Q2 are the charges after contact, then Qi/CI and Q2/C2 are the potential differences of the coatings and must be equal.
Hence Qi /CI =Q2/C2 or Q I /Q 2 =C I /C 2.
The mathematical importance of this function called the potential is that it is a scalar quantity, and the potential at any point due to any number of point charges ql, q2, q3, &c., distributed in any manner, is the sum of them separately, or qi/xl+q2/x2+q3/x3+&c. =F (q/x) =V (17), where xi, x2, x 3, &c., are the distances of the respective point charges from the point in question at which the total potential is required.
Let qi, q2,..
Pn, qn lie within a range such that p t is between p i and pi +dpi qi „ „ qi „ qi +dq i, and so on.
After a time dt the value of p i will have increased to pi+pidt, where p i is given by equations (i), and there will be similar changes in qi, P2, q2, ...
Thus after a time dt the values of the coordinates and momenta of the small group of systems under consideration will lie within a range such that pi is between pi +pidt and pi +dp,+(pi+ap?dpi) dt „ qi +gidt „ qi+dqi+ (qi +agLdgi) dt, Thus the extension of the range after the interval dt is dp i (i +aidt) dq i (I +?gidt).
From equations (i), we find that aq _ o a pi qi -, so that the extension of the new range is seen to be dp i dq i ...
Let us fix our attention on a small area dS of the boundary of the s (3) qi „ and so on.
In the modified problem where the loads W1 and W, on the two bars are replaced by loads P~, Qi, and P2, Q~ respectively, acting on the pins.
X=~-ql +~-qi +...
Theory of Vibrations.If, in a conservative system, the configuration (qi, q2, -..
However slight these forces may be, the total energy T+V must continually diminish so long as the velocities qi,q2,.
In discussing the small oscillations of a system about a configuration of stable equilibrium it is convenient so to choose the generalized co-ordinates qi, q2,..
T (qi, qi, - - - q,,)
= ai,Qi + aiyQz +...
Long rod-like form con QI a a taining a spore (these b II, .
1 19d'e:qi?l1, 1"i 1 pp II 11 1 111' 1 I III ' '11111 ?
What was new was that Wesley added an organization, Methodism (qi;), in which each of his followers unfolded to one another the secrets of their heart, and became accountable to his fellows.