Suggestions fur simplifying the Double Altitude Piobkm. 167 



found from time to time in the old caverns or weeldons of the 

 limestone. These acknowledged evils undoubtedly affected 

 the oecononiy and prosperity of the trade, until some more for- 

 tunate or more ingenious worker applied the bellows to the 

 art of iron-making, which gave rise to the blast bloomery, and 

 occasioned a great revolution and improvement in the fabrica- 

 tion of that valuable and highly useful metal. 

 Coleford, Gloucestershire. 



[To be continued.] 



XXVII. Suggestions for simplifijing Mr. Ivory's Solvtion of 

 the Double Altitude Problem. Bij Mr. Edw^ard Riddle, 

 Royal Naval Asylum, Grecjimch. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, — In The Philosophical Magazine for August 

 1821, Mr. Ivory has given a new and direct solution to the 

 well known nautical problem, which requires the latitude to be 

 determined from two altitudes of the sun, and the time elapsed 

 between the observations ; and as the rule which he has de- 

 duced possesses several advantages over any other that has 

 hitherto been given for the purpose, it may be hoped that 

 teachers of navigation will generally feel it tlieir duty to en- 

 deavour as much as possible to introduce it into practice. 



I conceive however Uiat, simple and convenient as the rule 

 is, its form yet admits of an advantageous alteration. In die 

 numerical calculation from the formulas which Mr. Ivory has 

 investigated, it is necessary to refer both to a table of natural 

 sities, and to one of the logarithms of numbers. But in this 

 solution of the problem, the use of both these tables may be 

 very easily dispensed with ; as by a simple transformation of 

 two of the expressions the wjiole of the calculations may be 

 performed with even greater neatness and lacility, with the aid 

 of no odier table than one of log. sines, &c. 



In a rule for the guidance of ordinary computers, it is de- 

 sirable to avoid, when it can conveniently be done, a reference 

 to a variety of tables; as the mere act of turning from one 

 table to another lias in itself a tendency to ])erplex. IJut by 

 the slight alteration whicli I have to propose in Mr. Ivory's 

 .solution, tliis objection to it (if an objection it may be called) 

 will be completely obviated; and, besides, the form of calcula- 

 tion admits of an exceedingly convenient arrangement; a cir- 

 cumstance which may recommend U»c rule to die attention of 

 persons who, otherwise, might not at once be sensible of its 

 value. JJ^ 



