32 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



repeat it with some detail. Given a horizontal plane; above 

 this plane, upon the same vertical and at known distances, 

 are placed two points, whose shadows upon the horizontal 

 plane can be followed. Around the common projection of 

 these points, as a centre, two arcs of circles are described, 

 whose radii are such that they can intersect the traces of the 

 shadows of the points themselves before and after the me- 

 ridian passage of the sun. The observation consists in meas- 

 uring the chords of the arcs obtained by joining the inter- 

 sections of the traces of the shadows with the circles; know- 

 ing the length of the chords, the radii of the arcs, and the 

 heights of the points whose shadows are observed, we can, 

 by a simple formula, calculate the latitude of a place. Either 

 the two points whose shadows are projected may be two 

 spheres, fixed upon the same vertical thread which traverses 

 their centres, or we may use small circular openings pierced 

 in metallic plates, and placed so that their centres are found 

 on the same vertical. The shadows of these objects are small 

 ellipses, whose centres may easily be found. The variation 

 in the declination of the sun, between the afternoon and 

 morning observations, occasions only a very small error, its 

 effect being, in great part, eliminated from the final formula. 

 The errors that may be made in measuring the various data 

 above enumerated can occasion very small errors in latitude. 

 The principal source of error is a possible want of exact hor- 

 izontality in the plane on which the shadow is cast. In fact, 

 an error of about two degrees in the inclination of this plane 

 may produce an error of one degree in latitude. If, however, 

 the plane be horizontal in a north and south direction, but 

 incline in an east and west direction, the effect of the latter 

 inclination may be neglected. The elimination of this latter 

 source of error is due in part to the adoption of two points 

 and shadows. The same advantages do not inhere in the 

 employment of one point and one shadow. Bulletin Ilcb- 

 domadaire, XV. ,578. 



DETERMINATION OF LATITUDE AND TIME. 



In a communication on the method of determining the 

 time by means of two observed altitudes of any celestial 

 body, Vice-admiral Von Wullerstorff-Urbair states that the 

 method of determining the latitude by means of observations 



