NATURE 



[May I, 1890 



principle as applied in acoustics, we find four cases: (i) 

 approach of observer, source and medium being at rest ; (2) re- 

 cession of observer, source and medium at rest ; (3) approach of 

 source, observer and medium at rest ; (4) recession of source, 

 observer and medium at rest. 



I have consulted all the standard authorities wfhich have 

 occurred to me, and find they all agree in the ist and 2nd cases. 

 In (3), Doppler, Lord Rayleigh, Prof. Everett (ist method in 

 " Deschanel "), Jamin, and Ganot have the same result as in (i). 

 Lord Rayleigh in his "Theory of Sound," vol. ii. p. 142, says, 

 " In the case of a periodic disturbance a velocity of approach v 

 is equivalent to an increase of frequency in the ratio a : a + v" a 

 being the velocity of sound. In another place the same author 

 says that it is the relative velocity of source and observer alone 

 that is important. The above-mentioned authorities appear to 

 hold the same views. 



But Prof. Everett has a more rigorous demonstration than the 

 above, which leads to the result — old pitch : new pitch '.: a-v.a. 

 This result is the same as that given by Mach, "Ton u. 

 Farberanderung durch Bewegung " (1874), and as that used by 

 Balfour Stewart, " Treatise on Heat." 



In the 4th case the first mentioned authors again agree, 

 giving as a result — new pitch : old pitch :: a : a- v. Prof. 

 Everett's and E. Mach's results agree in giving « + z> : « as the 

 ratio. 



It will be readily admitted that the first two cases are simpler 

 problems to attack than the last two. The results of the 

 minority for the cases (3) and (4) seem to me to come from 

 looking at the change in wave-length first, those of the 

 majority from taking into account the number of waves met by 

 the observer. In any case the disagreement among such 

 authorities is naturally beyond me to explain. The motion of 

 the medium does not appear to offer any special difficulty. 



G. H. Wyatt. 



The Relative Prevalence of North-east and South-west 

 Winds. 



The direction of the wind has been noted twice daily at 

 this Observatory (9 a.m. and 9 p.m.) during the past 6 years, 

 with the following mean results : — 



N. N.E.' E. S.E. S. S.W. W. N.W. Calm. 

 56 48 30 25 23 65 45 60 13 



The period under consideration is not sufficiently long to 

 make the series of observations of any great value, but as Mr. 

 Ellis asks for comparison'^, I am happy to give them for what 

 they are worth. C. E. Peek, 



Rousdon Observatory, Lyme Regis, April 26. 



The London Mathematical Society's List of Papers. 



In Nature (vol. xli. p. 594) it is stated that "a complete 

 index of the papers printed in the Proceedings of the London 

 Mathematical Society has been issued." It will be in the 

 recollection of some that a previous issue of the Index to the 

 papers contained in the first 17 volumes was announced in 

 Nature (vol. xxxvi. p. 42) : it is a re-issue of this list com- 

 pleted for the first 20 volumes that is now noted. The 

 former edition of 3000 copies was soon dispersed, and resulted 

 in warm expressions of thanks from mathematicians, and also in 

 an increased sale of the Proceedings. If other Societies would, 

 in like manner, issue lists of the titles of papers printed in their 

 Proceedings, they would no doubt meet with a like reward. 

 All mathematicians, and others who are interested in mathe- 

 matical research, can have a copy on application to the Secre- 

 taries (22 Albemarle Street, W. ), or to the publisher (Francis 

 Hodgson, 89 Farringdon Street, E.G.). 



April 26. R. Tucker, Hon. Sec. 



THE UNITED STATES SCIENTIFIC 

 EXPEDITION TO WEST AFRICA, 1889. 



A S the work of the Expedition approaches conclusion, 

 -^^ I venture to hope that a brief partial recital of re- 

 sults may be worth notice in Nature, particularly as, 

 in many of the ports we have visited, English courtesy 



and English hospitality have contributed in large measure 

 to the facilities for prosecuting our work, not to say also 

 very greatly to the delight of doing it, 



I find it a trifle difficult to say just where to begin, but 

 Dr, David Gill, H.M. Astronomer at the Cape, comes 

 first to mind, and surely no one could have devoted him- 

 self more unsparingly to the interests of the Expedition 

 than he did during our stay of a fortnight and more at 

 Cape Town : and through his liberal provision for every 

 requirement of the observers, it became possible to swing- 

 the pendulums in the Royal Observatory buildings, the 

 same spot occupied in previous gravity-research at the 

 Cape. Had it been expedient to delay the Pensacola 

 longer, Dr. Gill's suggestion would gladly have been 

 acted upon, and an additional gravity-determination 

 made at the Kimberley diamond fields, 650 miles in the 

 interior, at an elevation of about 4000 feet ; but there 

 was time only for members of the Expedition not engaged 

 in exact measures to proceed as far inland as that ; and 

 the movements and operations of the naturalists and 

 others who desired to visit the Cape Colony country as 

 far as Kimberley became feasible through the kind offers 

 of Mr. Difford, the Secretary of the Colonial Government 

 Railways. 



Not only at Cape Town had we much occasion to 

 thank His Excellency Sir H. B. Lock, the Governor of 

 the Colony, but two months later, at Ascension Island, 

 through his courteous intervention, and the obliging 

 civilities of Admiral Wells, R.N., all possible preparation 

 had been made ; while, on our arrival, Captain Napier, 

 R.N., in charge of Ascension, most thoughtfully smoothed 

 the way by arranging to our entire satisfaction all matters 

 which could in any way facilitate the work we had planned 

 for that interesting island. 



Nor am I forgetting the multitude of courtesies at the 

 hands of Governor Antrobus of St, Helena, where all 

 desired assistance was afforded, and where work similar 

 to that at Ascension was undertaken and completed. 



In this connection, I must not omit mention of the 

 American Navy, for neither the Expedition in its present 

 form nor its work could have become an accomplished 

 fact but for the enlightened policy of Secretary Tracy, 

 who assigned a man-of-war for its transport to Africa and 

 home again ; of Admiral Walker, and later. Commodore 

 Dewey, Chiefs of Naval Bureaux, who devoted their 

 energies ungrudgingly to the regulation of all matters 

 official affecting the welfare of the Expedition ; and of 

 Captain Yates, the commander of the U.S.S. Pensacola, 

 who has done everything in his power to forward the 

 prosecution of the scientific work. 



The Pensacola left N ew York on October 16 last ; called 

 at the ports of Horta, Fayal, Azores, November 2-3 ; San 

 Vicenti, Cape Verdes, November 10-12 ; St. George's 

 Parish, Sierra Leone, November 18-20; Elmina, Gold 

 Coast, November 26-28 ; Sao Paolo di Loanda, December 

 6-7 ; Eclipse Bay, Cape Ledo, December 8-27 ; again at 

 Loanda, December 28-January 6 ; Cape Town, January 

 17-February 6 ; St. Helena, February 20-March 10; and 

 arrived at Ascension six days later, which port she will 

 probably leave about April 10. 



Now to some of the results. 



At all these stations except Cape Ledo, the magnetic 

 elements have been carefully investigated by Mr. Preston, 

 of the U.S. Coast and Geodetic Survey. Also he had an 

 additional magnetic station at Cabiri, about 45 miles 

 interior from Loanda, whither he went for the immediate 

 eclipse period. 



The short time available before the eclipse made it im- 

 practicable to begin the gravity-determinations until 

 Loanda ; there Mr. Preston swung the Peirce pendulums, 

 and again at the Royal Observatory, Cape Town. At 

 St. Helena two complete swings were obtained, the one 

 at a sea-level station near the Castle, Jamestown, and 

 the other at Longwood, elevation 1750 feet. It was not 



