of Action between Magnets. 117 
Combining the vibration and deflexion experiments, omitting 
temperature and induction corrections, we find 
i 14 Pr-?+ Qr-4*=3(H°T?/21)r* sin u, 
_where T denotes the time ef a half vibration (rest to rest), 
and I the moment of inertia of the collimator magnet. The 
other letters have the same signification as before. 
Assuming T and wu cor rectly measured, we may for the 
present inquiry put 
Gear sire Bie iG. C10) 
and treat B as a constant. Also if B,, B,, B; refer to the 
three observation distances, we have as a first approximation 
+ aetigs Pr—? and Qr-‘ are always small compared with unity) 
By? = = Das =—H-?, : ° e ° (11) 
We can use (11) in small terms, after differentiation. 
From three equations of the type 
H?B— Pr —Qr-t=7-°, 
we find 
H?= (r.2—737) (79 —7)(rP—r?)+D, . . . eens dil? |. eee 
—P= {ry' (734 —7r')By + 79° ( ry t#—3t) Bo +1'3'(1'94 Bayt - ‘ (13) 
Q=r/r, 22 tr? (73” Farag (1) Bi +7” (Ge nara Oar, ?\Bo+73° AE orem (14) 
where 
=a oy veg —?1,") B, a ri (rye — 73”) ‘Bs a rd Cr —7,")B,. ° (15) 
Supposing 7; alone to vary, we find from (12) and (15) 
H dr; ey re—r? Pe — Ps 
7718 (73?-—757) By + 2r 1” o By—27,7,'B, 
Py (73? = 79”) By + 79' (7? — 7,7) Bo +27? — 177) Bs 
In this use Bee eee eee =e 
after reducticn we find 
ys dH 9 9 9 9 
an, = ON ele ne—n)} 
ry 3:42 *: 73 ° from (11), and 
This will sufficiently illustrate the mathematical operations 
necessary in obtaining the following results. 
Supposing 67;, 67, 673 small independent increments in 
11, To) 13, we find theicorr esponding increments in = EE 
