4.64, REPORT—1904. 
double contact with a fixed conic and touching the curve is 2(z +m): the number 
of conics through a fixed point having double contact with a fixed conic and oscu- 
lating the curve is 2(8 + 1), &c. 
The intersections of the other circular lines through the intersections of a curve 
with the circular lines through any point A (the satellites of A) play an important 
part in the theory of curves, especially when A is a focus. For example :—At 
bicircular quartics through four fixed points, A, B, C, D, having B as a focus 
whose satellite is A, pass through a fifth fixed point and have four-point contain 
with the osculating circle at A. 
The locus of the vertices of the common self-conjugate triangle of any oscu- 
lating conic through two fixed points and of a fixed conic through these two 
points is of degree 2(3u+1), class 2(2n+4m+kx), and has 2(11m+3:) inflexions. 
This is an extension of the theory of evolutes. 
The 7-th positive pedal of a curve is of degree 2(7—1)n+27m, class 
rn + (7 +1)m, and has (37 + 1) inflexions, &c., &c. (7 >1). Since the 7-th negative 
pedal of a curve is the inverse of the 7-th positive pedal of the inverse curve, we 
can readily deduce the properties of negative pedals from those of positive pedals. 
4. Note on a Special Homographic Transformation of Screw System 
Ly Sir Ropert Bart, LL.D., FBS, 
5. The Theory of Vibrations. By Professor V. VOLTERRA. 
6. The Stability of the Steady Motion of a Viscous Fluid. 
By Professor W. McF, Orr. 
7. Note on the Schwarzian Deriwative. By Professor A. C. Dixon, 7.2.8. 
8. Note on the Theory of Continuous Groups. 
By Professor A. R. Forsyru, L228. 
9. Some Observations on Linear Difference Equations. 
By Rev. E. W. Barnes. 
10. On the Use of Divergent Series in Astronomy. By Z. U. AHMAD. 
= ooqr ce 
MONDAY, AUGUST 22. 
The following Papers and Reports were read :— 
1. Recent Improvements in the Diffraction Process of Colour 
Photography. By Professor R. W. Woop. 
