38 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Trautwine's Pocket-Book for Eugineers was first written as a protest 

 against mathematics. It was a great help for a certain class of engineers, 

 for it gave them the results of the work of mathematicians which they 

 could not comprehend. It was also a help to engineers who were mathe- 

 maticians, but who had forgotten some of the formulte. What is now 

 needed is a handbook which shall also express the mathematics in as clear 

 a form as the results were expressed in Trautwine's book, and some 

 progress has already been made in tliat direction. 



The principles of Chemistry are as capable of cartographic representa- 

 tion as those of any other science. Mr. Sleeper of Jersey City appears 

 to be doing good work in this direction. 



In 1854, Dr. J. P. Cooke, our late President, prepared a table showing 

 the relation of the properties of the elements to their atomic weights, in 

 connection with a paper published by our society. Dr. Cooke then said : 

 " To my mind chemistry will then become a perfect science when all 

 substances have been classed in a series of homologues, and when we can 

 make a table which shall contain not only every known substance, but 

 also every possible one, and when by means of a few general formuUie 

 we shall be able to express all the properties of matter, so that, when the 

 series of the substance and its place in the series are given, we shall be able 

 to calculate, — nay, predict its properties with absolute certainty." 



Dr. Cooke's formula (a + n d) expressed the same idea, — viz. the 

 regular increase in the scale of atomic weights in each series, — whereas 

 the law of the octaves of Newlands and Mendelcyeff only admits of seven 

 elements in each period, and is inconsistent with this regular increase, 

 which, as every new discovery tends to show, lies at the foundation of 

 atomic chemistry. 



All sciences owe a debt of gratitude to the naturalists for developing 

 methods of classification that have been applied with such success. The 

 advantages of public museums are too well recognized to require 

 comment. 



Of all sciences Geography was perhaps the first to be thoroughly ex- 

 pressed by the cartographic method. A picture suggests a map, and a 

 map representing the prominent natural features suggests a map showing 

 the political divisions of the land, the distribution of animal and vegetable 

 life, etc. Geological Maps show the distribution of rocks, and Historical 

 Maps the distribution of political supremacy at different ages. 



I have already had the pleasure of calling the attention of the Academy 

 to my own work in preparing a series of maps, designed to show the 

 political divisions of Europe in every decade, or even at shorter intervals, 



