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III. On the Application of the Theory of Error to Cases of Normal Distrihution and 
Normal Correlation. 
By W. F. Sheppard, M.A., LL.M., Formerly Felloiv of Trinity College, Cambridge. 
Communicated by Professor A. R. Forsyth, F.R.S. 
Received (uDder the title On the Geometrical Treatment of the ‘ Normal Curve ’ of Statistics,” &c.) 
October 9, 1897,—Read November 25, 1897,—Revised July 15, 1898. 
Contents. 
Section. Page. 
Introductory. 102 
Part 1.—General Properties of the Normal Curve and op Normal Distributions. 
The Normal Curve. 
1. Definition of normal curve. 104 
2. Formation of family of curves by projection. 105 
3. Limitation to carves so obtained. 105 
4. Standard normal curve. 105 
5. Moment-formulse. 106 
The Surface of Revolution of the Normal Curve. 
6. Projective solids and surfaces. 107 
7. Normal solid and normal surface. 108 
8. Normal solid is projective solid. 108 
9. Converse pi’opositions. 109 
10. Value of C. Ill 
11. Representation of segment of normal solid by au area. Ill 
General Theorems relating to Normal Distributions. 
12. hlean squares and mean products of composite measures. 114 
13. Independent normal distributions. 114 
14. Correlated normal distributions. 117 
Part II. —Theory of Error. 
15. Distribution of linear function of errors of random selection 
16. Tendency of distribution to become normal. 
17. Probable error and jirobable discrepancy. 
. 117 
. 119 
122 
15.12.98 
