872 Intelligence and Miscellaneous Articles. 



time of Murchison onwards has been traced, and in particular 

 the relation of the Tarannon to the Llandovery and the Birkhill- 

 G-ala rocks is discussed in detail. In view of the occurrence of 

 two distinct facies (graptolitic and shelly) of the Valentian rocks, 

 two separate classifications are in use. The succession of grapto- 

 lites is made the basis of one of these classifications, the series 

 being divided into a Lower or Birkhill stage and an Upper or Gala 

 stage, each of which is further divided into substages and zones. 



The mixed facies of Grirvan allows certain shelly horizons to be 

 brought into relation with the graptolitic scale. Some of these 

 horizons were examined by the author in order to determine their 

 exact position on that scale, and the results of that investigation 

 are recorded in the paper. The fauna of various districts where 

 the shelly facies prevails is then compared with the Grirvan 

 succession. These districts include Haverfordwest, Llandovery. 

 Corwen and Grlyn Ceiriog, and the area's which lie between Shrop- 

 shire and the Mendips. On the basis of these comparisons a 

 general correlation-table of the Yalentian rocks is proposed, the 

 ro'cks of the shelly facies being divided into two stages — Lower 

 and Upper Llandovery, to the latter term being given a more 

 precise signification than has been the custom hitherto. 



It is suggested that the use of the term ' Tarannon,' which has 

 been the source of so much confusion in the nomenclature, be 

 discontinued, for the reason that it has proved to be equivalent 

 on the one hand to the Gala, and on the other to the Upper 

 Llandovery, as used in this paper. The base-line of the Yalentian 

 Series, also, is discussed in the light of recent work in Central 

 Wales and elsewhere ; and it is considered that in most districts 

 there is evidence of an abrupt lithological change at a certain 

 horizon, which in some cases amounts to a marked palseontological 

 break. The phenomena at that horizon are suggestive of arrested 

 sedimentation, if not also of actual erosion. 



XCVT. Intelligence and Miscellaneous Articles. 



To the Editors of the Philosophical Magazine. 

 Deae Sirs, — 



THE method of mental multiplication described by Mr. V. A. 

 Bailey in the September number of the Phil. Mag. was 

 published by me, in substantially the same form, in the issue of 

 'Nature' of November 26th, 1891 (p. 78). In reply to my 

 inquiry whether it had been known previously, Dr. K. Haas 

 stated (' Nature,' Dec. 31st, 1891) that it was mentioned by 

 Pappus as an invention of Apollonins (of Perga, born B.C. 262), 

 and was known to the Hindus (date not given) under the name of 

 Vajrabhyasa.' 



,_ _ -, tt /« . Yours very truly, 



18 Cainpden House Chambers, ^ a,' 



1 w 8i Olive Cuthbertsok". 



Se'pt.9tb, 1921, 



