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SCIENCE 



[N. S. Vol. XLIV. No. 1134 



1593 and followed by three Dutch editions be- 

 tween 1600 and 1607, by nine French editions 

 between 1602 and 1607, by four German be- 

 fore 1627, and by several other English edi- 

 tions. In this, following the conclusion that 

 the Pope is Antichrist, the end of the world 

 is set to fall between 1688 and 1700. This 

 type of arithmetical mysticism in the study of 

 " Revelations " appealed to many other mathe- 

 maticians of the sixteenth and seventeenth 

 centuries, some of whom were not so wise as 

 to set the end of the world sufficiently distant 

 to be safe. 



From the time of the earliest known trigo- 

 nometrical tables of Hipparchus and Ptolemy, 

 probably based upon Babylonian documents, 

 down through the ages there has been a con- 

 tinued interest in such mathematical tables. 

 The Babylonians, the Greeks, the Hindus, the 

 Arabs, the Europeans of the Middle Ages, and 

 many of the nations of the present day have 

 contributed energetic workers to this field. 

 !No one can deny to Napier the just claim to 

 having made the greatest contribution for the 

 final construction of tables sufficient for com- 

 putation purposes of the most diverse types. 

 Louis C. Kaepinski 



Univebsity of Michigan 



A NEW TRIANGULATION SIGNAL LAMP 



State, county and city surveyors must look 

 to the national government for the exact geo- 

 graphical positions upon which to base their 

 respective surveys. The duty to establish and 

 furnish these positions devolves upon the 

 United States Coast and Geodetic Survey. 



The geodesist determines astronomically 

 with the greatest possible exactness the longi- 

 tude and latitude of selected principal points, 

 suitably distributed over the whole country. 

 The geographical positions of the many places 

 between these principal points required are as- 

 certained most accurately and economically by 

 means of what is called triangulation. A 

 rough, preliminary or reconnaisanee survey re- 

 veals those points which are intervisable and 

 most desirable as to distance and other char- 

 acteristics, to form the corners of connected 

 triangles. From the measured length of one 



side of a suitably selected one of these tri- 

 angles and the angles of all the interconnected 

 ones, the exact latitude and longitude of each 

 point is computed. 



Though the general principle employed in 

 the measurement of these angles is the same 

 as that applied in the survey of a railroad, a 

 farm, etc., the great distance between the 

 points, varying between ten and a hundred 

 miles or over, requires not only the use of 

 specially large and refined instruments, but 

 also a special means of making the point vis- 

 ible to the observer. This latter is now done, 

 in day time, by reflecting sunlight to the ob- 

 server from a mirror placed accurately over 

 the point, and at night by means of a specially 

 constructed acetylene lamp. 



It is apparent that distances of the magni- 

 tude mentioned can be penetrated by either 

 means only under favorable weather condi- 

 tions, and that many days during a season are 

 lost even when the atmosphere is only slightly 

 clouded by smoke, fog, etc. As the expense to 

 maintain the party, which amounts to from 

 $50 to $60 per day, goes on whether observa- 

 tions are made or not, it was thought that ad- 

 vances in illuminating devices made since the 

 lamp now used was adopted might be utilized 

 to increase considerably the intensity of the 

 light directed to the observer, and thereby in- 

 crease the number of observing nights. 



Experiments made with calcium light pro- 

 duced by the oxy-acetylene flame showed this 

 form of illumination to be impracticable by 

 reason of cost and bulkiness of the apparatus 

 necessary. 



The storage cell was studied with the view 

 of using electricity as a source of light. Its 

 cost and weight and the difficulties connected 

 with its maintenance were found to be too 

 great. The electric generators with the neces- 

 sary prime motor were carefully studied, tried 

 experimentally and found to be too heavy for 

 transporting to difficult stations, and doubtful 

 as to continued and unfailing service. 



The result of a series of tests of dry cells, 

 which are readily divisible into loads suitable 

 for climbing difficult ascents, however, war- 

 ranted the design and construction of a new 



