Calendar: 1871-1872 Page 519

GENERAL LITERATURE AND SCIENCE 519 If be in harmonic progression then 2a 2c and £ £ 10 An event has happened which must have arisen from one of given number of causes required the probability of the existence of each of the causes Out of bag containing four sovereigns and eight shillings two coins are taken at random what is the value of the expectation 11 Prove the following sin ''" sin β cos cos β cos sin γ β sin sin cos cos β cos γ 27 cos12 cos-1 -cos-18 3C0s If α β sin sin β -f sin tan tan tan -- -' --'--'-- cos cos cosy 12 If sin β cos β sin and then cos β lab or a2 A2 c2 13 Show that in general the increment of the tabular logarithmic cosine of an angle is approximately proportional to the increment of the angle 14 If ra rj be the radii of the circles escribed with respect to the sides and respectively of triangle then s2 η tan η where is the semi-perimeter