due to Elasticity of the Earth's Surface. 423 



say at St. Alban's Head. He finds, then, that the deflection 

 of the plumb-line as high tide changes to low would be 

 4 0oo~oo °f ^ ne un ^ angle, or O^'OSO. The general theorem 

 proved above, as to the proportionality of slope to attraction, 

 shows that, with rigidity 3 x 10 8 for the rocks of which the 

 earth is formed, the apparent deflection of the plumb-line 

 would amount to W'2h. 



It is just possible that a way may in this manner be opened 

 for determining the modulus of rigidity of the upper 100 or 

 200 miles of the earth's surface, although the process would 

 be excessively laborious. The tides of the British Channel 

 are pretty well known; and therefore it would be possible by 

 very laborious quadratures to determine the deflection of the 

 plumb-line due to the attraction of the tide at any time at a 

 chosen station. If, then, the deflection of the plumb-line could 

 be observed at that station (with corrections applied for the 

 positions of the sun and moon), the ratio of the calculated to 

 the observed and corrected deflection, together with the known 

 value of the earth's radius and mean density, form the mate- 

 rials for computing the rigidity. But such a scheme would 

 be probably rendered abortive by just such comparatively 

 large and capricious oscillations of the vertical as we, M. 

 d'Abbadie, and others have observed. 



It is interesting to draw attention to some observations of 

 M. d'Abbadie on the deflections of the vertical due to tides. 

 His observatory (of which an account was given in the Report 

 for 1881) is near Hendaye, in the Pyrenees, and stands 72 

 metres above and 400 metres distant from the sea. He 

 writes* : — 



•"tFaireuni 359 comparaisons d'observations speciales faites 

 lors du maximum du flot et du jusant ; 243 seulement sont 

 favorables a la theorie de l'attraction exercee par la masse des 

 eaux, et l'ensemble des resultats pour une difference moyenne 

 de marees egale a 2*9 metres donne un resultat moyen de 

 0"'56 ou 0^'lS pour le double de l'attraction angulaire vers le 

 Nord-Ouest. Ceci est conforme a la theorie, car les differences 

 observees doivent etre partagees par moitie, selon la loi de la 

 reflexion ; mais comme il y a toujours de l'inattendu dans les 

 experiences nouvelles, on doit ajouter que sur les 116 compa- 

 raisons restantes il y en a eu 57 ou le flot semble repousser 

 le mercure au lieu de Fattirer. Mes resultats ont ete con- 

 tinues pendant l'hiver dernier par M. l'abbe Artus, qui a eu 

 la patience de comparer ainsi 71 flots et 73 jusants consecutifs, 

 de Janvier a mars 1880. Lui aussi a trouve un tiers environ 



* "Recherches sur la Verticale," Ann. de la Soc. Scient. de Bruxelles, 

 1881. 



