\ 
* 
344 On the Variation in the Length of the Day. 
Arr. XVII.—On the possible Variation in the Length of the 
Day, or of the Times of Rotation of the Earth upon its Azis; 
by W. W. Marner, 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.* Itis 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 ded 
ced, iserroneous in two particulars, and the calculation based 
upon it is necessarily wrong. The proportion alluded to is as 
follows : wt : 9 :utit3 0.” The two last terms of this 
miles, 
4 
proportion should have been t' : t, whence t’ a = st sa56)"= 
23h 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 1/ 27” 31” less than 
our day, on the assumption that the times of rotation are propol 
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. ¢. 
Beck, 1 vol. 4to, Part IV. Geology—Part Ist, Geology of Ist District, by Wn. 
W. Mather, 1 vol. 4to; Part 2d, Geology of 2d District, by E. Emmons, 1 vol. Ato; 
Part 3d, Geology of 3d District, by L. Vanuxem, 1 vol. 4to; Part 4th, Geology of 
4th District, by J. Hall, 1 vol. to. Part V. Paleontology of the State, by J. Hall, 
1 vol. 4to. Part VI. Agriculture of the State, by E. Emmons, 1 vol. 4to. 
