proceedings: philosophical society 105 



cians as an example of the application of the theory of functions of a 

 complex variable. This simple example of the broad subject of con- 

 formal mapping of one surface upon another deserves careful considera- 

 tion l)y all who wish to get a thorough grasp of the subject that is so 

 important in the natural sciences as well as in pure mathematics. x\ll 

 honor is due the Alsatian Lambert for his perception of the important 

 features of such a method of projection. However, even he did not 

 dream of the importance that the conformal relationship was to assume 

 both in pure and applied mathematics. 



Discussion: The paper was discussed by Messrs. Sosman, Harris, 

 LiTTLEHALEs, and Jones. 



]Mr. William Bow^ie presented a paper on Primary triangulation and 

 precise leveling as done by the United States Coast and Geodetic Survey. 

 The paper was illustrated by lantern slides and by three reels of moving 

 pictures which showed the instruments used in the precise leveling and 

 primary triangulation and the amount of work that has been done in 

 the United States, and also the methods of carrying on the various 

 operations. 



There have been completed to date about 38,000 miles of precise 

 leveling and 14,200 linear miles of primary triangulation and primary 

 traverse. These operations give standard elevations and geographic 

 positions throughout the country which are used by surveyors and 

 engineers for the control of their operations, especially in the map 

 makmg of the country. The work is of particular value in State and 

 international boundary surveys. 



Three reels of motion pictures were shown; one gave an excellent 

 idea of the methods employed by an up to date precise leveling party. 

 As now conducted, the precise level is mounted on a small motor veloci- 

 pede which runs on the railroad track. The instrument is mounted 

 on the car in the morning and it is not dismounted until the day's 

 work is completed. It is not even removed when the car is lifted from 

 the track to allow trains to pass. The recording of the rod readings 

 ig now done on a listing adding machine which is mounted on a second 

 motor car. 



Improvements recently made in the methods of organizing and 

 conducting the precise level party made it possible to increase greatly 

 the rapidity with which this work is done. The maximum progress 

 made by a precise leveling part}^ in any one month was 159.6 miles of 

 completed line. Each mile of this was leveled over at least twice. 

 The total number of single miles of leveling in that month was 324. 

 As much as 20 miles of single line were leveled in one day of seven 

 hours of actual observing. 



The second reel showed the erection of the towers or signals which 

 are used in triangulation in a wooded or flat country to elevate the 

 instrument to sufficient height to make it possible to observe from one 

 point to another. The length of lines of the triangulation varies from 

 a minimum of about 4 miles to a maximum of something over 100 

 miles. The signal is a double structure, consisting of an inner tripod 



