Calendar: 1873-1874 Page 554

554 APPLIED SCIENCES If is right angle show that sin Ε sin sin £ sec 19 If the sides of spherical triangle be small compared with the radius of the sphere then each angle of the spherical triangle will exceed by of the spherical excess the corresponding angle of the plane triangle the sides of which are of the same length as the arcs of the spherical triangle 20 Β is an arc of great circle of sphere and 2γ is its middle point and point Ρ is taken so that AP BP la Prove that cos2a sin AP sin BP cos'y sin'Oi is constant for all positions of IV department of ttjc pplteii Sbn'ences JStbtmtn Show that the government of Eli and Samuel marks transitional epoch between the period of the Judges and that of the Kingdom Trace the progress of the wars with the Philistines under Eli Samuel and Saul Examine the meaning of the word Prophet and the nature of the Prophetic Office in its relations to the Law the Priesthood and the Kingdom In what respects was the desire for King natural and pro- vided for by the Law and in what points lay its error and sin In what spirit did Samuel accept it Describe the character of Saul illustrating your answer from the history but not giving any continuous narrative What was the effect of his reign on the National power and character Give brief sketch of the life of David up to the time of his first accession to the throne What excellences and what defects are already marked in his character