ABSTRACTS 



Authors of scientific papers are requested to see that abstracts, preferably 

 prepared and signed by themselves, are forwarded promptly to the editors. 

 The abstracts should conform in length and general style to those appearing in 

 this issue. 



GEODESY. — General theory of polyconic projections. Oscar S. Adams. 

 U. S. Coast and Geodetic Survey, Spec. Publ. 57. Pp. 174. pi. i. 

 figs. 48. 1919. 



In this publication an attempt has been made to give a fairly com- 

 plete treatment of the various systems of projection in which the 

 parallels are represented by a group of non-concentric circles with the 

 centers of these circles all lying upon a straight line. The number of 

 such systems is unlimited; the aim has been, therefore, to give a de- 

 velopment of the projections that are most frequently met with in 

 practice. Some attention, however, is given to more general theoretical 

 considerations in order to illustrate the way in which particular prop- 

 erties can be attained in a given projection by the introduction of ana- 

 lytical conditions in the mathematical definition of the projection. 



In the treatment of any particular projection, the development is 

 given first from the standpoint of the simpler geometrical or analytical 

 principles upon which it is based, and later the same results are deduced 

 from the more general principles that may be found to apply to the 

 projection under consideration. This method of attack is found more 

 rigidly applied in the case of the conformal polyconic projections than 

 in the treatment of any other class in the polyconic group. The com- 

 paratively simple geometrical or analytical development is first given 

 and this is followed by a development of the results by the employment 

 of functions of a complex variable in accordance with the principles 

 demonstrated by Gauss and Lagrange, 



A full mathematical treatment of the ordinary or the American 

 polyconic projection is given in the latter part of the volume. No 

 adequate development of this has ever before been given in one volume 

 in an American publication. Information in regard to it has been 

 largely confined to articles in the various annual reports of the Super- 

 intendent of the U. S. Coast and Geodetic Survey, and the result has 

 been that it was difficult to get copies of the articles on account of the 

 exhaustion of the supply of the reports in which the articles were found. 



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