ON THE MEASUREMENT OF THE LUNAE DISTURBANCE OF GRAVxTT. 117 



If then the deflection of the plumb-line could be observed at that station 

 (with corrections applied for the positions of the sun aud 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 materials 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 meters above, and 400 meters distant, from 

 the sea. He writes : ' — 



' J'ai reuni 359 comparaisons d'observations speciales faites lors du 

 maximum du flot et du jusant ; 243 seulement sont favorables a la theorie 

 de I'attraction exercee par la masse des eaux, et I'ensemble des resultats 

 pour une di2"erence moyenne de marees egale a 2'9 metres donne un 

 resultat moyen de 0''-56 ou 0""18 pour le double de I'attraction angulaire 

 vers le Nord-Ouest. Ceci est conforme a la theorie, car les diS'erences 

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

 mais comme il y a toujours de I'inattendu dans les experiences nouvelles, 

 on doit ajouter que sur les 116 comparaisons restantes il y en a eu 57 ou 

 le flot semble repousser le mercure au lieu de I'attirer. Mes resultats ont 

 ete confirmes pendant I'hiver dernier par M. I'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 de cas defavorables a nos 

 theories admises. On est done en droit d'afiirmer que si la mer haute 

 attire le plus souvent le pied du fil a plomb, il y a une, et peut-etre 

 plusieurs, autres forces en jeu pour faire varier sa position.' 



We must now consider the vertical displacement of the land near the 



coast. In (21) it is shown to be ciq = ^— x ~ x 2-1037, where a^ 



TTV Tt'^ 



<o in- 



dicates the displacement coiTesponding to z = 0, 



With the assumed values, h = 40,v = 3 X 10^ 7 = 6-28 X 10^, I 

 find oq ^ 5'684 cm. Hence the amj^litude of vertical displacement is 

 11"37 cm. As long as M remains Constant ' this vertical displacement 

 remains the same ; hence the high tides of 10 or 15 feet which are actually 

 observed on the coasts of narrow seas must probably produce vertical 

 oscillations of quite the same order as that computed. 



If the land falls the tide of course rises higher on the coast line than 

 it would do otherwise ; hence the apparent height of tide would be h + oq. 

 But this shows there is more water resting on the earth than according 

 to the estimated value h ; hence the depression of the soil is greater in the 

 proportion 1 + uq/Ji to unity; this again causes more tide, which reacts 

 and causes more depression, and so on. Thus on the whole the augmen- 

 tation of tide due to elastic yielding is in the ratio of 



This investigation is conducted on the equilibrium theory, and it 

 neglects the curvature of the sea-bed, assuming that there is a uniform 



' ' Kecherches sur la Verticale,' Ann. de la Soc. Scient. de Bruxelles, 1881. 



