OCT. 19, 1921 abstracts: physics 417 



which is concave towards the equator. If an observed bearing is laid down 

 upon such a projection without correction, the line so determined is a tangent 

 to the great circle curve at its point of origin, because the Mercator projec- 

 tion is conform al. This publication gives a mathematical derivation of 

 the correction that must first be applied before the bearing is plotted on the 

 projection. A practical method is then devised so that the required cor- 

 rection may be determined by means of three graphic charts with as small 

 an amount of effort as possible. 



For convenience in application the description of the practical use of the 

 method is given first in the publication and the theoretical discussion is given 

 in the final part of the same for the benefit of those who may be interested 

 in this phase of the matter. A Mercator projection table for the sphere is 

 also included as it is of use in connection with the graphic charts, one of the 

 arguments for the same being obtained from it. 



On the gnomonic projection a great circle is represented by a straight 

 line, but the angle at the station is not preserved. It is necessary then for 

 any particular gnomonic chart to have a table computed for each radio- 

 compass station that gives the angles that must be laid off on the projec- 

 tion in order that the straight line may represent the great circle with any 

 given observ'ed bearing upon the earth. In this publication, tables are given 

 for ten radio-compass stations along the eastern coast of North America, 

 based upon the U.S.Hydrographic Office Chart No. 1280. O. S. A. 



PHYSICS. — The annealing of glass. L. H. Adams and K. D. Williamson. 

 Journ. Franklin Inst. 190: 597-631, 835-870. 1920. (Geophysical 

 Lab. Papers on Optical Glass, No. 32.) 



It is shown that the process of annealing glass can best be carried out if we 

 know for the various glasses and for the various temperatures the rate of 

 release of the internal stresses. The results of such measurements for nine 

 kinds of glass are presented. The release of stress at constant temperature 

 was found to proceed usually according to the equation 



F Fo 



in which F is the stress at any time, t, F^is the initial stress, and .4 is a constant 

 for the particular glass at a particular temperature, and is a measure of the 

 rate at which stresses are relieved. The variation of this rate with tem- 

 perature follows the equation 



log A = Mid — Ma 



in which Mi and Mo are constants for a particular glass and 6 is the tempera- 

 ture. 



At any temperature, a glass requires a certain annealing-time. This is 

 arbitrarily defined as the time required to reduce the stress (in optical units) 

 from 50 to 2>^ nn per cm. For convenience of reference, the 150° interval 

 of temperature lying immediately below the temperature at which the anneal- 

 ing time is 2 minutes is called (also quite arbitrarily) the annealing range. 

 At temperatures below the annealing range as thus defined, very little perma- 

 nent stress can be introduced. 



Concrete directions are given for annealing optical glass. The procedure 

 to be followed for other kinds of glass, such as plate glass, bottles, chemical 

 glassware, etc., is also indicated. Mathematical analysis of the problem shows 



