232 abstracts: navigation 



While adverting to the instances in which the spirit-level or liquid 

 column has been adapted to instruments similar to the sextant, the 

 main object has been to give an account of the evolution of a dynamical 

 artificial horizon for use at sea and, especially, of the gyroscopic horizon 

 designed as an attachment to the frame of the sextant of reflection. 



G. W. L. 



NAVIGATION. — Altitude, azimvith, hour angle. G. W. Littlehales. 

 Proc. U. S. Naval Inst. 43: No. 11. November, 1917. 



This paper presents a chart or diagram for finding, by a simple 

 graphic method, hour angle or azimuth at sea. This chart is based 

 upon the function of the angle called the haversine (half versed sine), 

 not generally employed outside nautical circles, and the formula used 

 as a basis is: 



hav(a) = hav(6 c) + hav(6 -\- c) — hav(6 « c) hav A 



If the sides, h, c, be regarded as constants, a, A, being variables, this 

 expression takes the form, 



y = mx + C 



which is the equation of a straight line. 



Based on this, a square chart is given, with sides graduated accord- 

 ing to values of a series of natural haversines, by means of which hour 

 angle and azimuth may be found, when the altitude and declination 

 of the body and the latitude of the place are given. By drawing a 

 straight line upon such a chart through two points easily determined, 

 a connection is established between hour angle and zenith distance 

 on the one hand, and between azimuth and polar distance on the other. 

 Hence, with either element of each of these two pairs given, the value 

 of the other may be taken from the chart. The chart itself is 2 feet 

 square and finely graduated so that it may be read with a great degree 

 of accuracy. 



The diagram is practical for finding azimuth in sea navigation, 

 and it is possible that in the future it may be adapted so as to be used 

 generally for hour angle purposes as well, especially when the naviga- 

 tion of the air becomes a matter of daily experience. J. F. Meyer. 



