Defence of English Periodical Mathematical Works. 369 



If Mr. Meikle will attempt the solution of some of those questions, 

 especially the last four, he will be much better employed than in 

 *• assisting Sisyphus in rolling his stone." This gentleman should 

 also recollect that an inquiry which, at first sight, appears merely 

 speculative, may ultimately be found of practical utility: of this 

 we have instances in the well-known application of Diaphantine 

 algebrse to the finding of fluents ; and still more recently in the 

 celebrated Gauss's successful application of a function derived 

 from arithmetical and geometrical progressions to some of the 

 most intricate though interesting problems in physical astro- 

 nomy. I am, sir. 



Yours respectfully, 

 London, Nov. 16, 1819. MathEMATICUS. 



Questions published inNo.Wl of Ladies' Diarij for 1820. 



1. What number is that which differs least from its common 

 logarithm ? and what number differs least from its hyperbolic 

 logarithm ? 



2. Given the segments of the base made by the perpendicular 

 from tbe vertical angle, to construct the plane triangle, when the 

 tangent of one of the angles at the vertex made by the perpen- 

 dicular has a given ratio to the sine of the other. 



3. A cistern containing 5236 cubic inches, being filled with 

 •water, had dropped into it five heavy balls, whose diameters were 

 5.n arithmetical progression. Required, the several diameters of 

 the said balls ; it being known that half the water was expelled 

 5n consequence of their immersion, and that the common difie- 

 lence of the terms of the progression was one inch. 



4. Find two integers, such that their sum shall be a square, and 

 their difference a cube number ; but, if each of them be doubled, 

 their sum shall be a cube, and difference a square number. 



5. The three edges of a triangular pyramid which terminate 

 in the vertex, are 12, 14, and 15; its perpendicular altitude 9; 

 and the edges of its base are as the numbers 2, 4, and 5. Now, 

 the distance of the centre of gravity from that angle of the base 

 where the longest slant edge meets the two longest sides of the 

 base being 6, what is the solidity of the pyramid ? 



6. Find the sides and areas, in whole numbers, of three scalene 

 triangles, such, that their perimeters shall be equal, and their 

 areas as the luunbers 2, 7, iind 15. 



7. Give, by means of right lines and a circle, a general con- 

 struction for the indeterminate equation a- — 2u{x-\-y)-\-x- + y^ 

 -fxy = o. 



8. A person has to cross an elliptical common, the axes of which 

 are eight and six miles, and has to call at a house situated in one 



Vol. 54. No. 259, Nov. 1819. A a of 



