(112 LAPLACE. 



Svanberg for deducing a result from observations made with a re- 

 peating circle : see Laplace's pages 82 — 35. 



Laplace explains a method of treating observations which he 

 calls the method of situation, and which he considers may in 

 some cases claim to be preferable to the "inost advantageous method 

 explained in his fourth Chapter. This method of situation had 

 been given in the Mecanique Celeste, Livre III., but without re- 

 ceiving a special name: see Art. 1016. Laplace gives an investi- 

 gation to determine when the inethod of situation should be pre- 

 ferred to the most advantageous method, and an investigation of the 

 value of a combination of the two methods. 



1051. The third Supplement is entitled A^yplication des 

 formules geodesiques de py^ohahilite, d la meridienne de France; 

 it occupies 36 pages: see Art. 928. 



Laplace begins by giving a numerical example of some of the 

 formulae in the second Supplement. In his pages 7 — 15 he gives 

 what he calls a simple example of the application of the geodesic 

 formulae. He takes a system of isosceles triangles, having their 

 bases all parallel to a given line, and he finds the errors in lengths 

 arising from errors in the angles. The investigation is like that in 

 the second Supplement. 



Laplace devotes his pages 16 — 28 to discussions respecting the 

 error in level in large trigonometrical surveys. 



Pages 29 — 36 contain what Laplace calls Methods generale du 

 calcul des prohabilites, lorsquil y a plusieurs sources d'erreurs. 



1052. Here we close our account of the Theorie Analytique 

 des Prohahilites. After every allowance has been made for the aid 

 which Laplace obtained from his predecessors there will remain 

 enough of his own to justify us in borrowing the words applied to 

 his Theory of the Tides by a most distinguished writer, and pro- 

 nouncing this also " to be one of the most splendid works of the 

 greatest mathematician of the past age." 



For remarks which will interest a student of Laplace's work I 

 may refer to the first page in the Appendix to De Morgan's Essay 

 on Probabilities .. .'va the Cabinet Cyclopaedia; to the History of the 

 Science which forms the introduction to Galloway's Treatise pub- 



