ehanioal Q 



IB appli arabe here dk I I may men- 



tion the dor. s ibility curve. B 



the more a<.- 2) to (7 it may he shown U 



/*[•-" ../'" -•"] =.'--- 





/*/ 



- be = L 



mooting it "-place values from Burg se si le were taken 

 and the result obtained coincided with \/y/~i accurately 



- This integral is of interest in the analysis of diffusion. 

 vies of the probability integral itself are commonly arrived 

 a somewhat intricate process, better fitted to yield a 

 e 1 set or - (ban a single one. Bv the formulae given 



in thi- ipplied to I - - - dated values of the prob- 



ability integral are readily determined.* 



imental physicists calculus is a thorn in the 

 and a wearine&E fet the spirit, partly, no doubt, 



stantij have to deal with functions whose mathe- 

 mati: 3&E ion is unknown or uncertain. I take leave to 



- s* that mechanical quadratures may serve them to reach 



visions which mathematicians would obtain n: . _.vntly 

 but in a If - he ~vav. 



But it appears to me that there is also room for a method- 

 ieal rxamination by mathematicians of the applicability of for- 

 mulae such as are developed in this paper to the integration of 

 functions which can not l:»e integrated in " finite terms." In 

 such an inquiry the main point would be to determine for each 

 - of functions the limits of convergence of Eider's series 

 and the nature of the substitutions most conducive to incs 

 in convergence. I hope somebody may pursue the matter 

 further. 



Wa,. _ D. C. April. 1911. 



*Fot jc= ' I .--- - table Ieuk. E. 5. Ed.. vol. xxxix. 1900, p. 257) 



a value of the probability integral greater by 2 in the seventh place 



than that wrignal :: :: in Encie'e taHe Ant Jahrbueh. Berlin, far 1834). 



nded i Kj ■ i_ - I - An _ -- It- : -r'fraetions astronomiqtie et 

 Paris, an Til [1779] ), and fa sheet "opted bv Airy. 

 -. and others. A physicist not familiar -with I rabies 



is — hich valne is correct, and this maybe a: 

 .-_.:' With h= ' -r^en-plaee values of j/=*-- 1 maybe 

 taken ont of Smithsonian Math. Tables. Integrating by [5) and multiplying 

 - . .rqnired integral at 77% 12 which is Burgess's value. 



If a : . t is available, the arithmetic is no more 



extended than in the example worked out in a previous footnote, and it re- 

 -laatieal know.- _ syond that required for interpolation 

 ■ • - -ponential. so that f. -:_ 

 eand. • nm" on a s.l i - _ Enote] aper. 



