VI 



CONTENTS. 



19. 

 20. 



21. 



22. 



23- 

 24. 



25- 



26. 



27. 



28. 

 29. 



so- 

 32. 



Exponential functions ^ . . 48 



Values of e^'^ and ^~* and their logarithms 



34- 

 35- 



36 



37 



38 



39 

 40 



41 

 42 



43 

 44 



45 

 46 



47 

 48 



49 

 50 

 51 



" " ^4 and^" " " " 



Vt — Vt 



" " dr~'^and ^ * "* " " 



" " e^ and <?~-^ and " " for fractional values of x 



Probability of errors of observations : probability integral 



Values of 0.6745 ^/ 



" " 0.6745 J-^^ 

 \n{ii—\) 



" 0.8453 



\n(n — i) 



" 0.8453 „^/ ■ 



;^2. Value for^ ^(i — sin26sin^<^)±id$ for different values of 6 ; also the cor- 



responding logarithms 



Moments of inertia, radii of gyration, corresponding weights 

 Strength of materials : (a) metals 

 (^) stones 



(<r) brick .... 

 (d) concretes . 

 " " *' timber tests 



Moduli of rigidity 



Variation of the moduli of rigidity with the temperature 

 Young's modulus ....... 



Compressibility of the more important solid elements 

 Hardness ........ 



Relative hardness of the elements 



Poisson's ratio ....... 



Elastic moduli of crystals, formulae 



" " " " numerical results 



Compressibility of O, air, N, H at different pressures and temperatures 

 " " ethylene " " 



" " carbon dioxide at " ** 



" ** gases, values of a . 



54 



55 



55 

 56 

 56 

 57 



57 

 58 

 58 

 58 



Least-squares formulae 59 



Inverse of probability integral. Diffusion 60 



Logarithms of the gamma function T{n) for values of n between i and 2 62 



Values for the first seven zonal harmonics from 6 = 0° to ^=90° . 64 



66 

 67 

 68 

 68 

 68 

 68 

 69 

 70 

 71 

 71 

 72 



73 

 73 

 73 

 73 

 74 



75 

 76 



76 

 76 



77 

 77 



