376 Mr. J. L, Hogg on Friction in 



+ j~-429^ +1287 3** -495^ 



+ 165 «_LY_ 6 ftI + ^ + 45^(11^ "-5 _^ 5 ) 



+ i 5 ? 1 ( 11 ^_3^) + 9^(-10ft^ + ^ 



a \ <2 S a o' a o #o a oJ «o 8 



+ 



The last equation is quite sufficient for relations involving 

 •experimental data. In many other cases, however, such for 

 example as the construction of mathematical tables, it is con- 

 venient to have the equation in the more extended form, and 

 thereby save the labour of making many tedious transforma- 

 tions, or of devising new methods for the development of the 

 inverse (or anti) functions. The second of the preceding- 

 problems is a case of this kind. Another important application 

 ■consists in being able to estimate, without reversion, the error 

 due to neglecting terms of a certain order in the reverse 

 series. For example, the error due to neglecting the term 

 in z 12 in problem (1) is of the order of magnitude of 

 58786 x 12" 11 x (2y) l \ or roughly 3 X lO" 4 ^ 12 , while the same 

 •error for problem (3) is approximately 6 x 10~~ 6 X y 12 . Since 

 in the first case y may exceed unity, the series will not 

 always suffice for computation, but in the second case 2/ = 0*l 

 and inspection shows that the remaining terms in the co- 

 efficient of z 12 will not greatly exceed 58786 X b u , consequently 

 the error arising from the omission of z 12 in this series 

 probably does not exceed 10~ 16 . 



U.S. Geological Survey, Washington, D.C. 

 October 1909. 



XXXVIII. Friction in Gases at Low Pressures. 

 By J. L.Hogg*. 



UNDER the title " Friction and Force due to Transpira- 

 tion as dependent on Pressure in Gases," there was 

 published f some time ago an account of some experiments 

 made to determine the relation between the friction of a gas 

 and the pressure in it, and also the relation between the 



* Communicated by Professor Trowbridge, 

 f Proc. Am. Acad. pp. 42-46 (1906). 



