F. GEOGRAPHY. 235 



list of altitudes of 150 carefully located points. Those es- 

 pecially interested in the paper will find it in the Report of 

 the United States Geological and Geographical Survey un- 

 der Professor F. V. Hayden for 1873. 



THE BATHOMETER OF DR. C. W. SIEMENS, F.R.S. 



In a report to the Secretary of the Navy on the Loan 

 Exhibition of Scientific Instruments at South Kensington, by 

 Professor E. S. Holden, U. S. N., are some interesting remarks 

 upon this ingenious instrument. 



Professor Holden says : The best description of this instru- 

 ment is to be found in Nature for March 30, 1876, from 

 which the following account is taken : A paper has been 

 presented to the Royal Society " On .determining the depth 

 of the sea without the use of the sounding-line," by Dr. C. W. 

 Siemens, who gave at the meeting of the 24th of February, 

 1876, a description of the instrument which he has designed 

 with this object. He commenced by giving a mathematical 

 statement of the effect of local attraction, to a certain depth, 

 on a body placed at the surface of the earth, assuming it to 

 be of uniform density, spherical in form, and unafiTected by 

 centrifugal action. For small values of depth (A) this at- 

 traction is 27rA. The original formula from which this is ad- 

 duced is; 



27rA 



and by substitution of 272 for h in this, Newton's statement 



4 

 of the total attraction -Rtt is obtained. 



Now, if in place of the solid substance which forms the 

 exterior crust of the earth, whose density may be taken to 

 be the mean density of superficial rock, water, a material of 

 less density, is substituted, it is shown that the total attrac- 

 tion must be diminished, and the measure of this diminution 

 is a measure of the depth of light substance which has been 

 substituted for heavy. If we were in possession of the exact 

 mean density of the earth, of that of the surface-rock, and 

 of sea -water, a scale could be calculated beforehand to 

 show what depth would agree with a certain diminution of 

 the measured eff*ect of gravitation. Such an approximate 



