# Calendar: 1854-1855 Page 357

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GENERAL LITERATURE AND SCIENCE 359 If χ τ &c to η terms n2 מ find Two vessels sail uniformly and ע knots an hour along lines inclined at an angle when they started their distances from the point of intersection of their courses are find their distance from each other when they are equi-distant from the point of intersection If it be possible and if χ ν x2 λ 2ע κ2 show that χ ν and Find the co-efficient of χ 271 in the product of λ2 χ4 x3 xr 273 2JAl &c7 If the terms of the expansion of where η is an integer be respectively multiplied by 71 η η ד י י- &c Λ Ο r2 find the sum of the series Transform 34 13 from the senary to the septenary scale 10 Show that fraction -f- the fraction inverted is how then can we assume χ cos 61 χ 11 Out of fixed sum of money η persons receive £100 annually one of them dies annually when it is found that the money lasts twice as long as was expected find the original fund and number of persons 12 given quantity is divided into an odd number of parts the sums of the first and second of the second and third of the third and fourth and so on and also of the first and last are known find the parts 13 Find three square numbers in arithmetical progression 14 Given log 7128 4334178 log 7129 4334339 find the log of 2712 856 15 Find whole number which is greater by unity than three times the integral part of its square root 16 hollow square and equilateral wedge each deep have

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