Tables 22 AND 23. EXPONENTIAL FUNCTIONS AND LEAST SQUARES. 47 

 TABLE 22. —Exponential Functions. 



Value of e' and e-" and their logarithms. 



TABLE 23. —Least Squares. 



Values oiV = ^f^"" e-C^r- d{hx). 



This table gives the value of P, the probability of an observational error having a value posi- 

 tive or negative equal to or less than x when h is the measure of precision, V = — f ^ e~ihx)i 

 d{hx). For values of the inverse function see the table on Diffusion. 



kx 



0.0 



.1 



-3 



•4 



0.5 



.6 



•7 

 .8 



-9 



1.0 



■3 



•4 



1.5 



.6 



•7 

 .8 



-9 



2.0 



-3 



-4 



2.5 



.6 



•7 

 .8 



•9 



3.0 



01 128 

 12362 

 23352 

 33S91 

 43797 

 52924 

 61 168 

 68467 

 74800 

 80 1 88 



84681 



8S353 

 91296 

 93606 

 95385 

 96728 

 97721 

 98441 



98952 

 99309 



99552 

 99715 

 99822 

 99891 

 99935 

 99961 

 99978 

 99987 



99993 

 99996 



99999 



02256 

 13476 

 24430 



34913 



44747 



53790 

 61941 



69143 



75381 

 80677 



85084 

 S8679 

 91553 

 93807 

 95538 



97804 

 98500 

 98994 

 99338 



99572 

 99728 



99831 

 99897 



99938 



99963 

 99979 

 99988 



99993 

 99996 



99999 



03384 

 14587 

 25502 

 35928 

 45689 



54646 

 62705 

 69810 



75952 

 81 1 56 



85478 

 88997 

 91805 

 94002 

 95686 



96952 



97884 



98558 



99035 

 99366 



99591 

 99741 

 99839 

 99902 



99941 



99965 

 99980 

 99989 

 99994 

 99997 



0451 1 



15695 



26570 



36936 

 46623 



55494 

 63459 

 70468 

 76514 

 81627 



85865 

 89308 

 92051 

 94191 

 95830 



97059 

 97962 

 98613 

 99074 

 99392 

 99609 



99753 

 99S46 

 99906 

 99944 

 99967 



99989 

 99994 

 99997 



44 

 89612 

 92290 

 94376 

 95970 

 ,97162 

 98038 

 98667 

 991 1 1 

 99418 



99626 

 99764 



99854 

 9991 1 



99947 



99969 

 99982 



99990 

 99994 

 99997 



06762 

 1 7901 

 28690 



38933 

 48466 



57162 

 64938 



71754 

 77610 



82542 



86614 

 89910 

 92524 



94556 

 96105 



97263 

 981 10 

 98719 

 99147 

 99443 

 99642 



99775 

 99861 



99915 

 99950 

 99971 



99983 

 99991 



99995 

 99997 



07886 

 18999 

 29742 

 39921 

 49375 

 579S2 

 65663 

 72382 

 78144 

 82987 



86977 

 90200 

 ,92751 



94731 

 96237 



97360 

 98181 



98769 

 99182 

 99466 



99658 

 99785 

 99867 

 99920 



99952 



99972 



99984 

 99991 



99995 

 99997 



8 



09008 

 20094 



30788 

 40901 

 50275 



58792 

 66378 

 73001 

 78669 

 83423 



90484 



92973 

 94902 

 96365 



97455 

 98249 

 98817 

 99216 

 99489 



99673 

 99795 

 99874 

 99924 

 99955 

 99974 

 99985 

 99992 



99995 

 99997 



10128 

 21184 



31828 

 41874 

 51167 



59594 

 67084 

 73610 

 79184 

 83851 



S76S0 

 90761 

 93 '90 

 95067 

 96490 



97546 

 98315 

 98864 



99248 

 9951 1 



99688 

 99805 

 99S80 

 99928 

 99957 



99975 

 99986 

 99992 

 99996 

 99998 



10 



1 1 246 

 22270 

 32863 

 42839 

 52050 

 60386 

 67780 

 74210 

 79691 

 84270 



88021 

 91031 

 93401 

 95229 

 9661 1 



97635 

 98379 

 ,98909 

 99279 

 99532 

 99702 

 99814 

 99886 

 99931 

 99959 

 99976 

 99987 

 99992 

 99996 



Taken from a paper by Dr. James Burgess ' on the Definite Integral _?- f ' e~^ dt, with Ex- 

 tended Tables of Values.' Trans. Roy. Soc. of Edinburgh, vol. xxxix, 1900, p. 257. 

 Smithsonian Tables. 



