326 CARNEGIE INSTITUTION OF WASHINGTON. 



Summaries of the results of the observations on the Carnegie on the present 

 cruise (No. IV) from Brooklyn to Honolulu and thence to Dutch Harbor, 

 Alaska, by the observing staff, J. P. Ault, H. M. W. Edmonds, I. A. Luke, 

 H. F. Johnston, and H. E. Sa^vyer. (Cf. pp. 320-322.) 



On the mean value of a function of spherical polar coordinates round a circle on a sphere. 

 H. Bateman. Terr. Mag. vol. 20, 127-129 (September 191.5). 



Some yeajs ago von Bezold pointed out that the mean value of the magnetic 

 potential round a parallel of geographical latitude is very nearly equal to a 

 constant multiple of the cosine of the north polar distance. Shortly after- 

 ward Adolf Schmidt considered the problem of finding the diameter of the 

 Earth for which the mean value of the magnetic potential round each small 

 circle with the diameter as axis, approximates in the best way to a constant 

 multiple of the cosine of the polar distance from one extremity of the diameter. 

 Schmidt chose as the criterion for obtaining the best approximation the con- 

 dition that the square of the difference between the two quantities just men- 

 tioned, when integrated over the whole Earth, should be a minimum. 



While reading Schmidt's paper, in connection with some studies at the 

 Department of Terrestrial Magnetism during the past summer, it occurred 

 to the author that it might be useful to have a simple formula for the mean 

 value of a function round a circle on a sphere. Such a formula can be deduced 

 without much trouble from the formulae for the transformation of spherical 

 harmonics in a transition from one set of polar coordinates to another. These 

 formulae have been given by Adolf Schmidt, but the particular theorem here 

 considered is not explicitly mentioned in his paper. A more direct proof of 

 the theorem is obtained in this paper by the use of a certain property of 

 potential functions. 



The Earth's Magnetism. L. A. Bauer. Ann. Rep. Smithsonian Institution for 1913. 

 Smithsonian Inst. Pub. 2281, 195-212, 9 pis. (1914). Washington. 



The fourth "Halley Lecture," delivered in the schools of the University of 

 Oxford on May 22, 1913; reprinted, after revision by the author and with 

 additional illustrations, from Bedrock, vol. 2, No. 3, October 1913, pp. 273-294. 

 The lecture concerns itself especially with Halley's contributions to terrestrial 

 magnetism, to recent advances relating primarily to the mapping of the 

 Earth's magnetic field at any one time, and to the determination of the secular 

 changes. Among the illustrations are a portrait of Halley, a view of the house 

 occupied by Halley while living at Oxford, and a reduced facsimile repro- 

 duction of Hallej^'s first chart of the lines of equal magnetic declination as 

 based on his observations in the Atlantic Ocean during the cruises of the 

 Paramour Pink, 1698-1700. In the closing paragraph the belief is expressed 

 that a long step forward will have been taken toward the discovery of the origin 

 of the Earth's magnetism when once we have found out the causes of its many 

 and often surprising variations — in brief, that "the keynote of modern investi- 

 gation in terrestrial magnetism, as in the biological sciences, must surely be 

 the study of the variations and mutations." Of what import the solving of 

 the riddles of the Earth's magnetism might be, is indicated to some extent by 

 Schuster's suggestive remark that "atmospheric electricity and terrestrial 

 magnetism, treated too long as isolated phenomena, may give us hints on 

 hitherto unknown properties of matter." 



On the Geographical Variation of the Earth's Magnetism. L. A. Bauer. 



This paper, which was read before section A (mathematics) of the American 

 Association for the Advancement of Science at the Philadelphia meeting in 

 December 1914, concerns itself chiefly with the question: Are the geographical 

 variations from the simple type of uniform magnetization parallel to a diameter, 



