>44 On the Variation in the Length of the Day. 



Art. XVII. — On the possible Variation in the Length of the 

 Day, or of the Times of Rotation of the Earth upon its Axis ; 

 by W. W. Mather, Professor of Natural History in Ohio Uni- 

 versity. 



Messrs. Editors — Will you permit me through your columns, 

 to correct an error and oversight in that volume of the Natural 

 History of New York, that treats of the geology of the first dis- 

 trict of New York.* It is too late to correct the errors in the 

 work itself, as it is published. A hasty preparation of the article 

 while the printers were waiting for copy caused one of the errors, 

 which any mathematical reader would detect at a glance. 



On the 638th page, a formula is given to show approximatively 

 the change in the length of the day, or of the period of a revo- 

 lution of the earth on its axis, upon the hypothesis of a variable 

 diameter of the globe at different periods of time. 



The proportion there stated, from which the formula is dedu- 

 ced, is erroneous in two particulars, and the calculation based 

 upon it is necessarily wrong. The proportion alluded to is as 



1 1 



follows: "— : -jj'.'.v : v'y.t : t'." The two last terms of this 



miles. 



tr'* * (3955)* 

 proportion should have been V \ t, whence 2'=— - =24/oQcg\ 4 " = 



23^ 58' 32" 29'". 



The time of a rotation of the earth on its axis, when consid- 

 ered as a sphere, with a radius one mile less than the present 

 mean radius, would be 23* 58' 32" 29"' or V 27" 31'" less than 

 our day, on the assumption that the times of rotation are propor- 

 tional to the fourth power of the radii. It is believed that the 



* The arrangement of the work on the Natural History of New York, published 

 under the authority and at the expense of the state, as the final report on the 

 " Geological Survey," is as follows, viz. — 



Part I. Zoology of the State, by J. E. Dekay, 6 vols. 4to. Part II. Botany of 

 the State, by J. Torrey, 2 vols. 4to. Part III. Mineralogy of the State, by L. C. 

 Beck, 1 vol. 4to. Part IV. Geology— Part 1st, Geology of 1st District, by Wm. 

 W. Mather, 1 vol. 4to ; Part 2d, Geology of 2d District, by E. Emmons, 1 vol. 4to; 

 Part 3d, Geology of 3d District, by L. Vanuxem, 1 vol. 4to; Part 4th, Geology of 

 4th District, by J. Hall, 1 vol. 4to. Part V. Palaeontology of the State, by J. Hall, 

 1 vol. 4to. Part VI. Agriculture of the State, by E. Emmons, 1 vol. 4to. 



