VOL. Lr.] PHILOSOPHICAL TRANSACTION^. 507 



therefore, that water, as well as ice, when in small quantities, with difficulty 

 transmits the concussion. Hence I suspected that a great quantity of ice would 

 permit an easier transit, which was indeed proved by experience, though 

 hitherto without using a piece larger than to give a shock to the elbows. 

 But, of equal quantities of water and ice, the ice transmits the less. 



LXXXI. Some Consideratums on a late Treatise intitled, A new Set of Loga- 

 rithmic Solar Tables, ^c. intended for a more Commodious Method of finding 

 the Latitude at Sea, by Two Observations of the Sun. By H. Pemberton, 

 M.D.R.S. Lond. et R.A. Berol S. p. 9 10. 



As it happens not unfrequently, at sea, for the unseasonable intervention of 

 clouds to prevent the ordinary method of determining the ship's latitude by the 

 sun's meridian altitude, even when it is of primary consequence that the true 

 latitude should be known ; a problem for remedying this disappointment is 

 stated in many treatises of navigation, for finding the latitude of a place by any 

 two altitudes of the sun, with the interval of time between them. A problem 

 similar to this is proposed, and solved instrumentally on a globe, by a very 

 early writer, Petrus Nonius, namely, to find the latitude by two altitudes of 

 the sun, and the angle made by the azimuth circles passing through the sun, 

 when the altitudes are taken. And since more commodious and accurate in- 

 struments for measuring time have been invented than were known to this 

 author, the other problem has been proposed for the same purpose, of which 

 a construction on the principles of the stereographic projection of the sphere 

 is exhibitted by Mr. Collins, in his Mariner's Plain Scale new planed. And 

 as the direct hiethod of solving both these problems by numbers requires a di- 

 versity of trigonometrical operations, a set of tables has lately been published for 

 a more compendious way of computation in the problem, where the interval of 

 time was given, by which the ship's true latitude may be very expeditiously de- 

 rived from the ship's dead reckoning, provided the observations are made within 

 certain limits of time. 



But however worthy of notice this method may be, new tables for the purpose 

 are altogether unnecessary. It consists of two parts : the first computes, from 

 the latitude exhibited by the dead reckoning of the ship, the distance from 

 noon of the middle time between the observations, and thence the time of either: 

 the 2d operation computes, from one of these observations, what should be the 

 sun's meridian altitude, had the ship's reckoning given the true latitude ; but 

 if the latitude assumed from that reckoning is erroneous, the altitude thus com* 

 puted will not be comformable to it ; however, if the times for the observa- 

 tions are properly chosen, it will much better agree to the true latitude, 

 and thence the assumed latitude may be more or less corrected. 



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