3 c
Sir
According to my desire I have Receved from Mr Newton that kindeness of'f your promiss: which weare
Conserning that Small Table of'f mine wchwhich was of'f the North Star's Hourly Altitude & Azimuth
The Contents of'f wchwhich Answer is in theese Lines: Cambridge SeptSeptember 11th: 1678 Mr Storer I have Looked over your tables
of'f the North Star's hourly Altitudes & Azimuth: & doe not perceive but that they ar Suff'ficientlySufficiently Exact.
But if ytthat I should presisely have sett downe the the minnute & fractionall part of'f a minute as my Calculatioon Gave it & by the very same Radius by wchwhich
that table of'f the North Star's Azimuth was Calculated then it will shew it as followeth for those hours parts of a minute wchwhich is for yethe Hours of: & for yetheHours: : parts of a minminute But for the Hours of Both Sixes: wchwhich is the Stars distance from the pole: But if I should have beene so presise wthwith the degrees minutes & fractionall part of a Minute & so neare as was shewed by the calculation wchwhich would have beene To the Thousand part of'f a Minute or less: therfore I suppose it would have beene very Hard Tedious & Troblesome to have whrought the same so neare by the Altitude: as I did there without it & by such a duouble way of'f working that no Less then 4 Hours Azimuth was shewed by the produce of'f one simple multiplication casting away some five figures then Adding the Remainer To or Substracting from a Nother constant given Summ: which is allwayes the same for yethe Lat'Latitude & Hour given But for yethe said tables he wrighteth that he doth not perceive but that they ar Sufficently Exact: Onley whether the Rule which I have computed the tables therby be Mathematically exact so ytthat with without Error danger of'f error it may be used to Compute the Altitudes & Azimuths of'f Stars which ar very Remoate from the pole I he cannot tell that he wrighteth is onley to be knowne from the demonstration of'f the Rule grounded on Mathematicall principles for wchwhich I think this same of'f myne is & if he receve my Letter dated about SeptSeptember yethe 4 or 5th: he will see by it a table of'f the Sunn or Stars Hourly Azimuth for Every 4th degree of'f the Suns or Stars declination from yethe Equinoctiall to Eather north or South: wchwhich declinations is Remoat from yethe pole wchwhich I Calculated for yethe Latitud of'f wchwhich is shewedth very neare your Lat'Latitude at Cambridge Because he might the sooner Looke it over without troble any great troble for so it may chance ytthat he may have them Allreddye callculated for ytthat or your Lat'Latitude by him: But because I have beene at ytthat panes To make these tables universall being halfe Calculated for All Latitudes vizd: from yethe Equinoctiall To yethe Pole I shall Heare Lay downe the Grounds of'f theare proportions of'f the Suns or any Stars Hourly Azimuth
The use of'f these Tables is thus for yethe Sun or any Stars Hourly Azimuth for these Latitudes the Declination being given multiply the sum of'f the Root of yethe Hourly Azimuth, for yethe Hour & Lat'Latitude suppoased: by the Tangent of the Sun or Stars declination: Cutt of foure figuers To yethe Right hand from the product: The Remaner being added to or Substracted from the Equinoctiall hours Tangent of Azimuth: sheweth the Tangent of the hours Azimuth being counted from yethe East or West. Example Lat'Latitude : the Declination North I demand the Azimuth at :10 in yethe morning & :2: in the Affter noon: & at :6: in yethe mormorning & 6 past noone at 2. in the morning & 10 at night at theese six hours I demand the Sun or Stars Azimuth: Aganst yethe Lat'Latitude under yethe hour Three sums Heare I finded by Addition: SubstrSubstraction & yethe produce wchwhich sums sheweth yethe sheweth the TangtTangent of 6 Hours Azimuth Thus.
First I finde by Substracting : out of yethe yethe EquEquinoctiall TangtTangent Rest : wchwhich sum is the Tangent of for yethe Azimth:Azimuth of .10: mormorning & .2: past noon. Secondly I finde by Adding of — To — : facit : wchwhich Sum is the Tangent of : for yethe Azimth:Azimuth at 2 in yethe mormorning & at 10 at night. Lastly the halfe of — is — : wchwhich Sum is the Tangent of : for yethe Azimth:Azimuth at 6 in yethe mormorning & 6: past noone. Thus by this Rule you finde 6 Hours Azimuth pp the produce of one small multiplication: shewd by AdditioAddition SubstSubstraction & the Summm. Againe I demand the Azimuth for theese 4 Hours of the day or night vizd for yethe Hour of 9 in yethe mormorning or 3 past noone, 9 at nigh or 3 in mormorning The declinatdeclination , Lat'Latitude :
Heare I finde by substracting out of : Rest : wchwhich is the Tangent of : wchwhich is yethe Azimuth for 9 in yethe mormorning or 3 past noon. But if I Add to — : facit wchwhich sum is the Tangent of wchwhich is yethe AzimAzimuth at 3 in yethe mormorning or 9 at night for North declideclination. But yethe Contrary hours for South declination: thus you may doe for any of ytthat; said Latitudes to any Hour & declination. To finde the Tangent of the Equinoctiall Hours Azimuth is Thus: Multiplye the Tangent of yethe Hours distance from :6: by the Sine of yethe Latitude Cut of 4 figures & yethe Remaner is the Tangent of yethe Azimuth: the Radius being : To finde the Roote of Azimuth: or Tangent of of declination: Multiply yethe Cosine of yethe Latitude being doubled by the Secant of the hour Being counted from :6: Cutt of 4 figures to yethe Right hand from the product; then halfe the Remaner shall be the desired Summm for the Roote of yethe Hours Azimuth: Now if you Add or Substract this Root of yethe Hours Azimuth To the Tangent of the saide Equinoctiall Hours Azimuth it will shew the Tangent of yethe hours Azimuth for of Declination: Heare I have shewded the proportions by wchwhich I Calculated the Sun' & The North Star's Hourly Azimuth wchwhich I would have done when I sent Mr Newton my Last Table of yethe Sun's Hourly Azimuth wchwhich I could not then doe by Reason of yethe shortness of my Time: Therefore I would Intreat your favour if ytthat you pleace dTo do me that kindness once moore as to lett desire him to Looke over theese proportions To see whether they hold Good yea or not for I have bestoooed so much paines wthwith them. In the Same Manner as I have shewed you by the Tables Heare made universall: Tables for All Latitudes vizd from yethe Equinoctiall to yethe Pole. Therefore if Mr Newton could doe me ytthat faivour as to Resolve me of wchwhich in 6 or 8 dayes affter the dait of this He would much Oblidge me thereby: Haveing no moore at prsentpresent But Returning you many thancks for your Trouble & Great G kindeness at Boothby & Elcewhear with my True Love & Service To Mr Newton Returning him many thancks for his kindeness I Rest at yoryour Command your Nepheu to Seve you Arthur Storer
London SeptSeptember 19th: 1678
Thanckes be to God All wthwith us heare ar very well: hopeing yethe like wthwith you. I was wthwith Coz Wm King this day who is very well & I hope will do well. Both hee & Shee mindes there buisness very Cloacely & I hope ytthat he will have a very great helpe by her Especially in the Consernes of his trayde he imployeth a boy aprentice & a Jorneyman: All of wchwhich I finde usally very hard at worke.
For the Reverend Doct Humphry Babington at Trenitye Colidge In Cambridge 4