CONTENTS. 



18. Exponential functions . . . . . 48 



19. Values of e^ and e~ x and their logarithms . . .54 



H n 



20. " " e? and *"*"* " " " ...... 55 



21. " " e~*ande 4 ' " ...... 55 



22. " u ^ and e~ x and " " for fractional values of x . 56 



23. Probability of errors of observations : probability integral . . .56 



24. " " " " " " " 's? 



25. Values of 0.6745 */- 57 



2 7 . " " 0.8453 -T--v ......... 58 



29. Least-squares formulae ......... 59 



30. Inverse of probability integral. Diffusion . . .60 



31. Logarithms of the gamma function T() for values of n between i and 2 62 



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



/- 



33. Value for / 2 (i sin 2 0sin 2 </>)=Bd<l> for different values of ; also the cor- 



J o 



responding logarithms ......... 66 



34. Moments of inertia, radii of gyration, corresponding weights . '67 



35. Strength of materials : (a) metals ... . .68 



(b) stones . 68 



(c) brick .... ... 68 



(</) concretes ....... 68 



36. " " " timber tests 69 



37 " u' it n it .... 70 



38. Moduli of rigidity . . . 7 1 



39. Variation of the moduli of rigidity with the temperature . . 7 1 



40. Young's modulus ...... .... 72 



41. Compressibility of the more important solid elements . . 73 



42. Hardness -73 



43. Relative hardness of the elements ... -73 



44. Poisson's ratio '73 



45. Elastic moduli of crystals, formulae . .... 74 



46. " " " " numerical results . 75 



47. Compressibility of O, air, N, H at different pressures and temperatures 76 



48. " " ethylene " " " " " 76 



. Q (( (( U (( (( U t H^ 



50. " " carbon dioxide at " " " " . 77 



51. " " gases, values of a 77 



