GENERAL SUMMARY 



OF 



SCIENTIFIC AND INDUSTRIAL PEOGEESS 

 DUEING THE YEAE 1874. 



MATHEMATICS. 



In pure Mathematics we note the completion of the com- 

 putations of the tables of elliptic functions compiled at the 

 expense of the British Association, and the presentation to 

 the Royal Astronomical Society of an original computation 

 by John Thompson of the logarithms, to twelve places of 

 decimals, of all numbers up to 120,000. 



Mr. G. W. Hill offers a valuable suggestion in reference to 

 the use of the true anomaly in the computation of absolute 

 perturbations. The publication of Todhunter's "History of 

 Mathematical Theories of Attraction" is an event eminently 

 worthy of being noticed in this place. A well-considered 

 article in the North American Review, from the pen of Pro- 

 fessor Newcomb, lays bare the difficulties against which the 

 cultivators of pure mathematics and exact science have to 

 contend in this country, and will, it is to be hoped, stimulate 

 our national progress in that field. An interesting application 

 of pure mathematics to the problems of organic life is that of 

 Dr. Grabau on the spirals of the shells of the Ammonite ; he 

 shows that, if we allow for very slight errors of measurement, 

 it will be seen to be impossible to decide whether these ani- 

 mals build their shells according to the concho-spiral or the 

 logarithmic-spiral theories. 



A new mathematical society has been formed at Prague. 



A mathematical journal, The Analyst, has been publish- 

 ed during the year by Professor Hendricks, of Des Moines, 

 Iowa, which has contained interesting articles by Professor 

 A. Hall, G. W. Hill, and other mathematicians. This is the 

 only journal in the United States devoted to exact science. 



The invention bv Peaucellier of what he called his com- 



