Calendar: 1875-1876 Page 579

GENERAL LITERATURE AND SCIENCE 575 great circle passing through the fixed point prove that the equation of the great circle passing through the points β is cot φ sin β -f- cota sin β coti sin If χ he the length of the arc drawn from the fixed point per- pendicular to this great circle prove that sin2 β cot3 cot2a co ft 2cota cot& cos β -algebra anb 3Είμοη of Kquattone If ayz bzx cxy χ -y 2' each memher abc A- c2 24c 2ca 2ab Shew how to express given fraction by series of radix fractions in any proposed scale Transform 119716 into the scale and extract its square root in that scale Transform the square root back into the scale 10 If a2 a3 on be in Harmonical Progression prove that a2 a2a3 a1 11-1 a1an and a3 a2a4 an-2an £ a1a1- -j- β2β If χ be real prove that χ is never less than and that x2 χ2 χ lies between and Find the continued fractions equivalent to V37 and Λ