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For the Reverend Doct
Babington of Trinity
Colidge in Cambridge
diliver
{2}

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Sir    Returning you many thancks for your kindness I have Receved an Answer in part from Mr Newton which is that he hath tryed my Numbers & found them hold well: which hath Incoradged me once moore to present him with another Burd, of the same fether hatched at the said Time & I thinck as well Trimed & dect with fethers yett not Alltogether of so swifft a wing butt Fuly as many chaingeble Noates: I have Likewise a Great many moore such Like Tables which moast of them ar by duble wayes of working which I had Allmost filled a Book with which: which I thought once that it would have {comed} to Mr Newtons {wringh} & so thought affter His Examining to have brought it to perfection But now being other wayes Called of I am forced to Lett it Sleepe in Silence: Only I would desire him once moore to Looke over this Table that hee may see whether the proportions hold good {yea} or no: as I suppose they may or Else I have spent some time therin in vaine: I suppoase I shall not Receve an answer of which while I be in London for about Saterday or Munday next at the furthest I thinck that I shall take shipp & so fall doune to Graves End which perhapes if an answer Come soone I may Receive it there otherwayes it may be by affter ships: Haveing no moore at present but my service to Mr Newton & my Duty to your selfe with my prayer to God for your Long Life & Comffortabe dayes I Rest your Obedient Nephew

at your Command to Serve you / Arthur Storer

London October the 1st 1678:

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A Table to finde the Sun or any Stars Altitude uppon Every  5th  Azimuth from the East or West Eather Northward Or So_wardsOr to finde the Sunn or any Stars Altitude by proportion uppon any point of' the Compass Or uppon any AzimuthOr the Altitude & Azimuth Given to finde the Declination For the Latitude of 51 : 52 : 53 : 54 : 55 : &c :0 Azimuth________________________________________________________________________________________Degrees of the Azimuth________________________________________________________________________________________Azimuth ____________________________________________________________________________________________________________________________________________________________________________________________________________________________ ye  Latitude051015202530354045505560657075808590 ____________________________________________________________________________________________________________________________________________________________________________________________________________________________ ___________000000000000000The Equinoctiall Altitudes uppon these Azimuth in Degrs & min 5100=00·12868 04=02··12837 08=00·12744 11=50··12594 15=29·12400 18=5412174 22=0311927 24=5511671 27=3011414 29=48.·11167 31=4910935 33=3410723 Deg00 m35=02:10536: Deg00 min36=1610375 Deg0 min37=1610240 Deg00m38=0210136 Deg00 min38=34:10061 Deg00 min38=5410016 Deg00 min39=0010000 0 5200=00·12690 03=54·12661 07=43·12576 11=26·12439 14=57·12260 18=1712050 21=21·11820 24=08:11580 26=4011340 28=5511108 30=5410890 32=3710699 34=0610511 35=1810357 36=1710230 37=0210130 37=35·10058 37=5410015 38=0010000 0 5300=00·12522 03=46·12495 07=27·12416 11=02·12291 14=27·12126 17=4011920 20=39·11716 23=2311493 25=5111269 28=0311051 30=0010845 31=4110656 33=08·10486 34=2010340 35=1810220 36=0310124 36=35·10055 36=5410014 37=0010000 0 5400=00·12361 03=37·12336 07=11·12264 10=39·12149 13=57·11998 17=0411918 19=58·11617 22=3811410 25=0211200 27=11·.10995 29=0610801 30=4510623 32=1010462 33=2210324 34=1910210 35=0310119 35=35·10053 35=5410014 36=0010000 0 5500=00·12208 03=29·12186 06=56·12115 10=16·12013 13=28·11872 16=2911707 19=18·11523 21=5311329 24=1411133 26=20·.:10941 28=1210758 29=5010591 31=1410438 32=2410308 33=2110200 34=0410113 34=35·10051 34=5410013 35=0010000 Latitude0000000000000000000 51:7771::7790:784779408064821483848568876189559145932694919638976598669939998410000 5278807898795271398156829884608635881890039184935595149655977598729942998510000 5379868003805481368247838185358701887490499221938495369671978598779945998610000 5480908105815482318336846286078765892990959258941395589686979598839947998710000 55:8191:8252825283248423854286788827898291409295944295809701980598889949998710000 ___________0_________________________________________________________________________________________________________________________________________________________________________________________________________________

The use of this Table to finde the Sun or Stars Altitude uppon Every 5th Azimuth: for the Latitude of 51:52:53:54:55 Against the Latitude under the Degrees of Every 5th Azimuth to 90degrs: you will finde two sumes the first or uppormost sums Sheweth the degrees & minute of the Equinoctiall Altitude uppon that Azimuth the Next sums under which Being multiplyed with the :Sine: of the declination: cutt of foore figuers to the Right hand from the product: then the degree & minute of the sine of the Remainer Being Added to the degree & minute of the Equinoctiall Altitude sheweth the degree & minute of the Altitude uppon that Azimuth for North declination: But if you Substract it from the Equinoctiall Altitude the degree & Minute of the Remaner will shew the Altitude for that Azimuth for South Declination{.} Example Latitude 53: the declination 23degs=31min Eather North or South: I demaund the Sunn or Stars Altitude or depression uppon the 60: Azimuth Eather Northwards or Southwards from the East or west: I finde the summ for the Azimuth under the 60: Azimuth Against 53degs of the Latitude to bee :10486: which sum I Multiply by the Sine of 23degs=31min which is 1648603990_9437409437400031458000_facit —4183/9140 Rest Nearest 4184: whole sine is 24degs=44min which being Added to the Equinoctiall which is 33deg=0824deg=44facit —57deg=52 which 57degs=52min sheweth the Altituded uppon the 60th Azimuth Southwards of the East or west for north declination{.} But for South declination the depression uppon the 60th Azimuth Northwards of the East or West will be 57degs=52min{.}
But if I Substract my said sum which is 33d=0824d=44Rest —08d=24 Being the Suns Altitude uppon the 60: Azimuth Southwards of the East or West for South declination: which is his depression uppon that Azimuth for North declination Northwards &c, I Demaund the Altitude of Hercus & Lyra uppon the Afforesaid 60th Azimuth & Latitude ye  sum_  is —10486the declination of' hercus being  45degs=38min the sine theareof is  7149  wch  sum_  being Multiplyed thus —07149_facit —7496/4414 Rest 7496: the summ theareof is — 48degs=34min wch  being Added to33=0848=34facit for  ye  Altitude .81=42 which is Hircus {his} Altitude uppon the 60 Azimuth Southwards{.} But if I Substract thus 48`=3433`=08Rest —15`=26 Being the Altitude of Hircus uppon the 60th Azimuth North Wards
I demaund the Altitude of Lyra uppon the said 60th Azimuth the sum is 10486 which Summ I multiply by the sine of Lyras declination which is — 38=30 ye  sine of'  wch  is —006225_facit —6527/5350 Rest 6527 being  ye  sine of'40degs=45min33degs=08facit —73degs=53: the Altitude Being uppon that Azimuth Southwards of the East or West: But if you substract from40`=4533`=08Rest —07`=37 for the Altitude Northwards of the East or West {so} upon that Azimuth{.} The Like is to be Observed for the Sunn or any Other Star for Every 5th or 10th Azimuth Or by proportion to any degree of the Azimuth Or any point of the Compass If that you make proportion of boath summs: vizd that Sum of the Azimuth &: Likewise the degrees & minutes of the Equinoctiall Altitude &c{.}

The Next is the Altitude of the Sunn or Starr uppon any 5th Azimuth to finde the declination{.}

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For the Resolveing of this Question which is of Excelent use for the findeing of the Suns place in the Ecliptick Or his Longitude or the day of the Month Or the declination of any fixed star or the Latitude or declination of any plannet &c this Question being one of the three principall termes whearby is Resolved Moast of the Moast usuall problemes in Astronimy therefore I have at the bottom of the Aforesaid table under Every 5th or 10th Azimuth to 90degrs of Azimuth Given the proportionable summs whearby is found the Sunn or Stars declination{.} Example Latitude 53: I find the suns Altitude uppon the 60th Azimuth to be 57degs=52min Being southwards of the East or west I demand the declination the Altitud being57degs=52minthe Altitude of  ye  Equinoctiall uppon the  60th  Azimuth Southwards  wch  I substact is —33degs=08Rest —24degs=44 which 24degs=44min I finde the sine theareof to be 4184 which summ I sett doune then I Looke at the bottome of the table under the 60th Azimuth aganst the Latitude I finde the summ 9536 which summ I Multiply by 4184: which multiplyed by 9536: facit 3989/8624: Rest Nearest 3990: which is the sine of 23degs=31min the Declination desired{.} Againe the Altitude of Hircus uppon the Afforesaid 60th Azimuth being 81degs=42min Southwards for the East or west I demand the declination: the Equinoctiall Azimuth uppon that 60th Azimuth is 33degs=08min which I substract from 81degs=42min Rest 48degs=34min the Sine thereof is 7497· which being Multiplyed with the Sum of the Azimuth which is 9536: facit 7149/1392: Rest 7149: which is the Sine of 45degs=38min the declination desired:



To Calculate the Afforesaid Tables for the finding the Sun or Stars Altitude uppon any Azimuth: Or there Altitude uppon any Azimuth to find the declination{.} First for the Equinoctiall Altitude uppon any Azimuth Multiply the Tangent of the Complement of the Latitude Given By the sine of the Azimuth Given cutt of foare figuers to the Right hand: then the Tangent of the Remainer sheweth the Altitude uppon that Azimuth{.} Thus haveing found the Equinoctiall Altitude uppon the Azimuth Given: The Next is to finde the Second found Sum which Summs ar sett at the bottome of the Table for the most Redyest way of finding the Declination when the Altitude & Azimuth is Given: Which is thus found: Multiply the Secant of the Equinoctiall Altitude of that Azimuth Given by the sine of the Latitude Cutt of foare figuers to the Right hand from the product Then the Remainer is the Second found Summ: Example the Equinoctiall Altitude uppon the 60th Azimuth in the Latitude 53 is 33deg=08min the Secant thereof is — 11942: Which summ I Multiply by the Sine of 53degs=00: which is 1194207986_facit —9536/8812: Facit: Rest 9536: which is the Sum desired: Now the Altitude of the Sunn or any of the Said Stars might as well be found uppon the said 60 Azimuth as well by this Summ 9536: as well as by the Said Summ shewed befoare which weare 10486: Onley this performes the work by Multiplication but the Summ 9536 performes it by Division{.} Example the declination 23dr=31m the Sine I multiply per 10000 thus —39900000Quotient4183nearestthe Divisor is —9536 which sheweth the Sine of 24degrees=44min as beffore which Add & Substracted as before the worke is the same as shewed befoare for the Suns declination. But if that you would have the said sum 10486: & so performe the worke by Multiplication as shewed by the former Exampls Multiply the Radius by the Radius which is heare 10000 thus —100000000Quotient10486: —  wch  is the Afforesaid Summ defined &c.  the divisor is —9536



thus have I shewed 2 wayes for the finding of the Altitude of the Sunn or any Star upon Any Azimuth & that by a duble way of working so that the product of one Multiplication as shewed beffore will shew the Altitude uppon the Azimuth Lett it be Eather South East or South West Nor East or Norwest the declination being Eather North or South &c

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Professor Rob Iliffe
Director, AHRC Newton Papers Project

Scott Mandelbrote,
Fellow & Perne librarian, Peterhouse, Cambridge

Faculty of History, George Street, Oxford, OX1 2RL - newtonproject@history.ox.ac.uk

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