Drontheim　　　　　Sun　　　　　　　　　　　　　　　63　　25　　51。3　　　63　　26　　　6。1　　　14。8　　　　　　　　　　　　　　　Alph。Urs。Min。　　　　　　　　　　　　　57。2　　　　　　　　　　　49。4　　　　7。8
  This　presents　a　very　different　view　of　the　latitudes　as　determined　by　the　small　repeating　circle；　from　that　in　Captain　Sabine's　book；　and　confining　ourselves　still　to　Maranham；　where　the　latitudes　〃WERE　OBTAINED；　WITH　ESPECIAL　REGARD　TO　EVERY　CIRCUMSTANCE　BY　WHICH　THEIR　ACCURACY　MIGHT　BE　AFFECTED；〃　and　where　〃A　MORE　THAN　USUAL　ATTENTION　WAS　BESTOWED；〃　it　appears；　that　if　we　take　Captain　Sabine's　own　test；　namely；　〃the　differences　of　the　partial　results　from　the　mean　at　each　station；〃　the　deviations　become　nearly　ten　times　as　large　as　they　were　before；　a　circumstance　which　might　be　expected　to　have　some　influence　in　the　decision　of　the　question。
  There　is；　however；　another　light　in　which　it　is　impossible　to　avoid　looking　at　this　singular　oversight。　　The　second　column　of　the　table　of　latitudes　must　now　be　considered　the　true　one；　as　that　which　really　resulted　from　the　observations。　Now；　on　examining　the　column　of　true　latitudes；　the　differences　between　the　different　sets　of　observations　is　so　considerable　as　naturally　to　excite　some　fear　of　latent　error；　more　especially　as　nearly　the　greatest　discordance　arises　from　the　same　star；　Alph。Lyrae；　observed　after　an　interval　of　only　three　days。　　It　becomes　interesting　to　every　person　engaged　in　making　astronomical　observations；　to　know　what　is　the　probability　of　his　being　exposed　to　an　error　so　little　to　be　guarded　against；　and　so　calculated　to　lull　the　suspicions　of　the　unfortunate　astronomer　to　whom　it　may　happen。
  In　fact；　the　question　resolves　itself　into　this：　the　true　latitude　of　a　place　being　determined　by　sets　of　observations　as　in　the　first　of　the　following　columns
  Latitudes　as　True　latitudes　observed。　　　　　　　　　　　　　　　　　　　　　computed　by　a　mistake　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　of　Capt。　Sabine's。
  deg。min。sec。　　　　　　　deg。min。sec。　Alph。Lyrae；　28th　Aug。　。　。　。　　2　　31　　22。0　　　　　　　　2　　31　　42。4　Alph。Lyrae；　29th　Aug。　。　。　。　　　　　　　　　31。8　　　　　　　　　　　　　　　43。8　Alph。Pavonis；　29th　Aug。　。　。　　　　　　　　　44；0　　　　　　　　　　　　　　　44。5　Alph。Lyrae；　31st　Aug。　。　。　。　　　　　　　　　42。6　　　　　　　　　　　　　　　44。6　Alph。Cygni；　31st　Aug。　。　。　。　　　　　　　　　39。2　　　　　　　　　　　　　　　42。0　Alph。Gruris；　2d　Sept。　。　。　。　　　　　　　　　27。4　　　　　　　　　　　　　　　42。2
  what　are　the　chances　that；　by　one　error　all　the　latitudes　in　the　first　column　should　be　brought　so　nearly　to　an　agreement　as　they　are　in　the　second　column？　　The　circumstance　of　the　number　of　divisions　of　the　level　being　almost　arbitrary　within　limits；　might　perhaps　be　alleged　as　diminishing　this　extraordinary　improbability：　　but　let　any　one　consider；　if　he　choose　the　error　of　each　set；　as　independent　of　the　others；　still　he　will　find　the　odds　against　it　enormous。
  When　it　is　considered　that　an　error；　almost　arbitrary　in　its　law；　has　thus　had　the　effect　of　bringing　discordant　observations　into　an　almost　unprecedented　accordance；　as　at　Maranham；　and　not　merely　so；　but　that　at　eight　of　the　nine　stations　it　has　uniformly　tended　to　diminish　the　differences　between　the　partial　results；　and　that　at　the　ninth　station　it　only　increased　it　by　a　small　fraction　of　a　second；　I　cannot　help　feeling　that　it　is　more　probable　even　that　Captain　Kater；　with　all　his　admitted　skill；　and　that　Captain　Sabine　himself；　should　have　been　both　mistaken　in　their　measures　of　the　divisions　of　the　level；　than　that　so　singular　an　effect　should　have　been　produced　by　one　error；　and　I　cannot　bring　myself　to　believe　that　such　an　anticipation　is　entirely　without　foundation。
  Whatever　may　be　the　result　of　a　re…examination；　it　was　a　singular　oversight　NOT　TO　MEASURE　the　divisions　of　a　level　intended　to　be　used　for　determining　so　important　a　question；　more　particularly　as；　in　the　very　work　to　which　reference　was　made　by　Captain　Sabine　for　the　purpose　of　comparing　the　observations；　it　was　the　very　first　circumstance　which　occupied　the　French　philosophers；　and　several　pages　＇See　pages　265　to　275　of　the　RECUEIL　D'OBSERVATIONS　GEODESIQUES；　&c。　PAR　MM。　BIOT　ET　ARAGO；　which　forms　the　fourth　volume　of　the　BASE　DU　SYSTEME　METRIQUE。＇　　are　filled　with　the　details　relative　to　the　determination　of　the　value　of　the　divisions　of　the　level。　　It　would　also　have　been　satisfactory；　with　such　an　important　object　in　view；　to　have　read　off　some　of　the　sets　after　each　pair　of　observations；　in　order　to　see　how　far　the　system　of　repetition　made　the　results　gradually　converge　to　a　limit；　and　in　order　to　know　how　many　repetitions　were　sufficient。　　Such　a　course　would　almost　certainly　have　led　to　a　knowledge　of　the　true　value　of　the　divisions　of　the　level；　for　the　differences　in　the　altitude　of　the　same　star；　after　a　few　minutes　of　time；　must；　in　many　instances；　have　been　far　too　great　to　have　arisen　from　the　change　of　its　altitude：　　and　had　these　been　noticed；　they　must　have　been　referred　to　some　error　in　the　instrument；　which　could　scarcely；　in　such　circumstances；　have　escaped　detection。
  I　have　now　mentioned　a　few　of　the　difficulties　which　attend　Captain　Sabine's　book　on　the　pendulum；　difficulties　which　I　am　far　from　saying　are　inexplicable。　　He　would　be　bold　indeed　who；　after　so　wonderful　an　instance　of　the　effect　of　chance　as　I　have　been　just　discussing；　should　venture　to　pronounce　another　such　accident　impossible；　but　I　think　enough　has　been　said　to　show；　that　the　feeling　which　so　generally　prevails　relative　to　it；　is　neither　captious　nor　unreasonable。
  Enough　also　has　appeared　to　prove；　that　the　conduct　of　the　Admiralty　in　appointing　that　gentleman　one　of　their　scientific　advisers；　was；　under　the　peculiar　circumstances；　at　least；　unadvised。　　They　have　thus　lent；　as　far　as　they　could；　the　weight　of　their　authority　to　support　observations　which　are　now　found　to　be　erroneous。　They　have　thus　held　up　for　imitation　observations　which　may　induce　hundreds　of　meritorious　officers　to　throw　aside　their　instruments；　in　the　despair　of　ever　approaching　a　standard　which　is　since　admitted　to　be　imaginary；　and　they　have　ratified　the　doctrine；　for　I　am　not　aware　their　official　adviser　has　ever　even　modified　it；　that　diminutive　instruments　are　equal　almost　to　the　largest。
  To　what　extent　this　doctrine　is　correct；　may　perhaps　yet　admit　of　doubt。　　It　cannot；　however；　admit　of　a　doubt；　that　it　is　unwise　to　crown　it　with　official　authority；　and　thus　expose　the　officers　of　their　service　to　depend　on　means　which　may　be　quite　insufficient　for　their　purpose。
  How　the　Board　of　Longitude；　after　EXPRESSLY　DIRECTING　THIS　INSTRUMENT　TO　BE　MADE　AND　TRIED；　could　come　to　the　decision　at　which　they　arrived；　appears　inexplicable。　　The　known　difference　of　opinion　amongst　the　best　observers　respecting　the　repeating　principle；　ought　to　have　rendered　them　peculiarly　cautious；　nor　ought　the　opinion　of　a　Troughton；　that　instruments　of　less　than　one　foot　in　diameter　may　be　considered；　〃FOR　ASTRONOMY；　AS　LITTLE　BETTER　THAN　PLAYTHINGS；〃　＇Memoirs　of　the　Astronomical　Society；　Vol。I。　p。53。＇　to　have　been　rejected　without　the　most　carefully　detailed　experiments。　　There　were　amongst　that　body；　persons　who　must　have　examined　minutely　the　work　on　the　Pendulum。　　Captain　Kater　must　have　felt　those　difficulties　in　the　perusal　of　it　which　other　observers　have　experienced；　and　he　who　was　placed　in　the　Board　of　Longitude　especially　for　his　knowledge　of　instruments；　might；　in　a　few　hours；　have　arrived　at　more　decisive　facts。　But　perhaps　I　am　unjust。　　Captain　Kater's　knowledge　rendered　it　impossible　for　him　to　have　been　ignorant　of　the　difficulties；　and　his　candour　would　have　prevented　him　from　concealing　them：　　he　must；　therefore；　after　examining　the　subject；　have　been　outvoted　by　his　lay…brethren　who　had　dispensed　with　that　preliminary。
  It　would　be　unjust；　before　quitting　this　subject；　not　to　mention　with　respect　the　acknowledgment　made　by　an　officer　of　the　naval　service　of　the　errors　into　which　he　also　fell　from　this　same　level。　　Lieutenant　Foster；　aware　of　the　many　occasions　on　which　Captain　Sabine　had　employed　this　instrument；　and　knowing　that　he　considered　each　division　as　equal　to　one　second；　never　thought　that　a　doubt　could　exist　on　the　subject；　and　made　all　his　calculations　accordingly。　When　Captain　Kater　made　him　acquainted　with　the　mistake；　Lieutenant　Foster　immediately　communicated　a　paper　＇The　paper　of　Lieutenant　Foster　is　printed　in　the　Philosophical　Transactions；　1827；　p。122；　and　is　worth　consulting。＇　to　the　Royal　Society；　in　which　he　states　the　circumstance　most　fully；　and　recomputed　all　the　observations　in　which　that　instrument　was　used。　　Unfortunately；　from　the　original　observations　of　Mr。　Ross　being　left　on　board　the　Fury　at　the　time　of　her　loss；　the　transcripts　of　his　results　could　not　be　recomputed　like　the　rest；　and　were　consequently　useless。
  SECTION　5。
  OF　THE　UNION　OF　SEVERAL　OFFICES　IN　ONE　PERSON。
  Although　the　number　of　situations　to　which　persons　conversant　with　science　may　hope　to　be　appointed；　is　small；　yet　it　has　somewhat　singularly　happened；　that　instances　of　one　individual；　holding　more　than　one　such　appointment；　are　frequent。　　Not　to　speak　of　those　held　by　the　late　Dr。　Young；　we　have　at　present：
  MR。　PONDAstronomer　Royal；　Inspector　of　Chr