Xotices respecting Neio Books. 807 



nomial theorem from the law of virtual velocities, or make 

 the rule for the extraction of the square root flow as a eon- 

 sequence from Archimedes' law of floating bodies. 



Johns Hopkins University, 



Baltimore, Maryland, tf. S., 

 August 28, 1876. 



XXXVIII. Xotices respecting New B coles. 



Tables for facilitating Sumner's Method at Sea. By Sir William 

 Thomson. D.C.L.,LL.D., F.E.S., Professor of Natural Philosophy 



in the University of Glasgow, and Fellow of St. Peter's College, 

 Cambridge. London : Taylor and Francis, 1876. 



TX 1871 Sir William Thomson communicated to the Royal 

 -*- Society a paper which was published in its ' Proceedings,' 

 in which, after stating his decided preference for Sumner's over 

 any other method of reducing observations at sea, lie went on to 

 show how Tables might be prepared which would greatly shorten 

 and simplify the application of that method. He has had these 

 Tables calculated under the superintendence of Mr. Roberts, of the 

 Nautical-Almanac Office ; and they have been largely used by the 

 author and his friends during several years. These private trials 

 have served to prove the practical utility of Sir W. Thomson's 

 system, and to justify its publication. The Tables are now issued, 

 accompanied by Rules for their use, which are sufficiently explicit 

 to direct the sailor, even although he shoidd be ignorant of the 

 principles of the method he is applying. The method, however, is 

 folly explained in a preface to the book, which is of considerable 

 scientific interest, and of which we proceed to give a short abstract. 



Sir W. Thomson begins by pointing out that any single obser- 

 vation of the altitude of the sun or of a star at a known instant of 

 Greenwich time affords data for drawing on the earth's surface a 

 circle, at some point in which the observer must have been, and 

 from every point in which the altitude of the body observed was 

 the same at the time of the sight. Of course the body observed 

 must at that time have been vertically overhead of the centre of 

 this imaginary circle, and every part of the circle is perpendicular 

 to the true bearing of the body observed. All that any one ,: sight " 

 tells the sailor is that the ship is somewhere upon one such circle ; 

 and if he can actually draw a small portion of the circle (short 

 enough to be taken without sensible error as a straight line) in 

 that part of his working chart in which the ship is known to be, 

 he will have obtained all the information that the "sight" can 

 yield, and he will have expressed it in the most concise and scientific 

 form possible. The short straight portion of this circle, which it 

 is the object of Sumner's method to draw, is commonly called a 

 Sumner line. 



When an observation of time and altitude has been made, the 

 corresponding Sumner line may be drawn in either of two way-. 

 We may take two estimated latitudes, say the two integer degrees 

 nearest to the true latitude, and calculate the longitude corre- 



X2 



