A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

Mutual Power of Two Circles. 113
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Fig. 4
Fig. 44.
DEF. XXXVI.-The product of the cosines of the spherical
radii of two circles, subtracted from the cosine of the arcjoining
their spherical centres, gives a remainder, which is called the
mutual power of the two circles.?
If the circles be denoted by letters with suffixes, we shall
denote their mutual power by the suffixes. Thus the mutual
power of the circles Sa, sg shall be denoted by af/.
106. Frobenius's Theorem.-If s,, s5, s3, 84, s5; 8s1, 821> s3, s4, s8'
be any two systems of five circles on the sphere; then
11', 12', 13', 14', 15'
21', 22', 23', 24', 25'
31', 32', 33', 34', 35' = 0. (405)
41', 42', 43', 44', 45'
51', 52', 53', 54', 55'
DEM.-Let xi, y,, sz, &c., denote the normal co-ordinates of
the centres of the circles, with respect to a fixed trirectangular
* The introduction of this term into Geometry is due to DAIBOUX,
"Annales de l'École Normale Supérieure," vol. I., 1872.
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