For the Reverend Doct
Babington of Trinity
Colidge in Cambridge
diliver
2
Sir Returning you many thancks for your kindness I have Receved an Answer in part from
Mr Newton wchwhich is that he hadth tryed my Numbers & found them hold well: wchwhich hath Incoradgedged me once
moore to present him with with another Burd, of the same fether hatched at yethe 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 wchwhich moast of them ar by duble wayes of working
wchwhich I had Allmost filled a Book with wchwhich: wchwhich I thought once ytthat 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 ytthat 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 vaaine: chwhich while I
for about Saterday or Munday next at the furthest I thinck that I shall take shipp & so fall
doune to Graves End wchwhich perhapes if an answer Come soone I may Receive it there otherwayes it may
be by affter ships: Haveing no moore at prsentpresent 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 OctobrOctober yethe 1th1st 1678:
The use of this Table to finde the Sun or Stars Altitude uppon Every 5th Azimuth: for yethe Latitude of Against the Lat'Latitude under the Degrees of Every 5th Azimuth to : you will finde two sumes the first or uppormost sums Sheweth the degrees & minminute of the the Equinoctiall Altitude uppon that Azimuth the Next sums under which Being multiplyed with the :S'Sine: of the declination: cutt of fooore figuers to the Right hand from yethe product: then the degree & minute of the sine of the Remainer Being Added to yethe degree & minminute of the Equinoctiall Altitude sheweth the degree & minminute of yethe Altitude uppon that Azimuth for North declination: But if you Substract it from the Equinoctiall Altitude the degree & MinMinute of the Remaner will shew yethe Altitude for ytthat Azimuth for Southth Declinatioon. Example Lat'Latitude : the declination Eather North or South: I demaund the Sunn or Stars Altitude or depression uppon the : Azimuth Eather Northwards or Southwards from the East or west: I finde the summ for yethe Azimuth under the : Azimuth Against of yethe Lat'Latitude to bee :: wchwhich sum I Multiply by the Sine of wchwhich is Rest Nearest : whole sine is which being Added to yethe Equinoctiall wchwhich is wchwhich 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 yethe East or West will be . But if I Add Substract my said sum wchwhich is Being the Suns Altitude uppon yethe 60: Azimuth Southwards of the East or West for South declination: wchwhich is his depression uppon ytthat Azimuth for North declination Northwards &c, I Demaund the Altitude of Hercus & Lyra uppon the Afforesaid 60th &Azimuth & Lat'Latitude Rest : the summm theareof is — wchwhich is Hircus ishis Altitude uppon yethe 60 AzimAzimuth Southwards. But if I Substract thus Being the Altitude of Hircus uppon yethe 60th Azimuth North Wards I demaund the Altitude of Lyra uppon the said 60th Azimuth the sum is wchwhich Summ I multiply by the sine of Lyras declination wchwhich is — Rest yethe Altitude Being uppon ytthat AzimAzimuth Southwards of yethe East or West: But if you substract for yethe Altitude Northwards of yethe East or West so upon ytthat AzAzimuth. The Like is to be Observed for yethe Sunn or any Other Star for Every 5th or 10th Azimuth Or by proportion to any degree of the Azimuth Or any point of yethe Compass If ytthat you make proportion of boath summs: vizd ytthat Sum of the Azimuth &: Likewise the degrees & minutes of the Equinoctiall Altitude &c.
The Next is the Altitude of yethe Sunn or Starr uppon any 5th Azimuth to finde the declination. for
For the Resolveing of this Question wchwhich is of Excelent use for the findeing of the Suns place in yethe Ecliptick Or his Longitude or the day of the Month Or the declination of any fixed star or the Lat'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 of Azimuth Given the proportionableable summs whearby is found the Sunn or Stars declination. Example Lat'Latitude : I find the suns Altitude uppon yethe 60th Azimuth to be Being southwards of the East or west I demand the declination wchwhich I finde the sine theareof to be wchwhich summm I sett doune then I Looke at yethe bottome of the table under yethe 60th Azimuth aganst yethe Latitude I finde the summm wchwhich summm I Multiply by : wchwhich multiplyed by : facit : Rest Nearest : wchwhich is the sine of the Declination desired. Againe the Altitude of Hircus uppon the Afforesaid 60th Azimuth being Southwards formfor yethe East or west I demand the declination: the Equinoctiall Azimuth uppon ytthat 60th Azimuth is wchwhich I substract from Rest the Sine thereof is wchwhich being Multiplyed with the Sum of yethe Azimuth wchwhich is : facit : Rest : wchwhich is the Sine of 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 yethe Equinoctiall Altitude uppon any Azimuth Multiply the Tangent of the Complement of the Latitude Given By the sine of yethe Azimuth Given cutt of foare figuers to yethe Right hand: then the Tangent of yethe Remainer sheweth yethe Altitude uppon ytthat Azimuth. Thus haveing found the Equinoctiall Altitude uppon the Azimuth Given: The Next is to finde the Second found Sum wchwhich Summs ar sett at the bottome of the Table for yethe most Redyest g way of finding the Declination when the Altitude & Azimuth is Given: Which is thus found: Multiply the Secant of the Equinoctiall Altitude of ytthat Azimuth Given by the sine of the Lat'Latitude Cutt of foare figuers to the Right hand from the product Then the Remainer is the Second found Summ: Example yethe Equinoctiall Altitude uppon the 60th Azimuth in yethe Lat'Latitude is the Secant thereof is — : Which summ I Multiply by yethe Sine of : wchwhich is : Facit: Rest : wchwhich is the Sum desired: Now the Altitude of the Sunn or any of the Said Stars might as well be found uppon yethe said Azimuth as well by this Summm : as well as by the Said Summ shewed befoare wchwhich weare : Onley this perfomesperformes the work by Multiplication but yethe Summm performes it by Division. Example yethe declintdeclination yethe Sine I multiply pper wchwhich sheweth yethe Sine of as beffore wchwhich Add & Substracted as before the worke is the same as shewed befoare for yethe Suns declinatdeclination. But if ytthat you would have the said sum : & so performe the worke by Multiplication as shewed by the former Exampls Multiply the Radius by yethe Radius wchwhich is heare
thus have I shewed 2 wayes for yethe finding of yethe Altitude of the Sunn or any Star upon Any Azimuth & ytthat by a duble way of working so ytthat 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