From Archibald McLachlan   Sunday

50 Fanshawe S^t– Sunday

Dear T.

I have got into such a system of scribbling that I can’t break myself off it, the more I try to correct myself the worse I get, have you any secret by which I could correct this confounded scribble hand? – I wrote you a long and tedious scratch 3 or 4 days ago,¹ enclosing a trace – if you understand the trace tis all that can be expected – it might have been a little finer & plainer, but I had to trace it off in a hurry – or by stealth – I got another since, and would have sent it had I not got a letter yesterday from M^r Kelly² saying you were out levelling – You will have it in the course of this week – I saw my learned man,³ we discoursed of Tides on sea and land; he says there is a book written wherein is described all manner of curves, indeed it is from this book, or the principles laid down there, that the whole system of representing political, religious, and philosophical progress by curve lines – the book is called – ‘Quetelets System of Nature’⁴ price 1/6 – Chambers’s Edition for the people – You could easily get in Manchester – there is a great Socialist bookseller in Manchester, from him you can get any book – up near the Infirmary, or Hospital at the reservoir a good way farther up than the postoffice – when you walk up to the Post office keep it on your right hand, and go on til you come to the Pond or reservoir, keep that on your right also, and go on 100 or 150 yards, turn off to the left – (the infirmary is then behind you) go down a long street, go down about 250 or 300 yards and on your right hand is the Shop – the Name is – Heywood⁵ –

My learned man plotted the curves of life and Death taken from the Data furnished by the Irish Census – the Census of Dublin City – and others – one line of curves was plotted for all Ireland – one for the City of Dublin – all these will be published when the Irish Census &c is Complete – The outlines of mountains – Waves of the Sea – Lives of men – women – Diseases – Deaths – Crime – poverty – ignorance – all can be shown better by Curved lines than any other way – because at one glance you can have all the lines before your eye – just as you have a number of Waves of the sea – you can see how the curves run parallel or cross – or separate – and by simply looking on the lines you can tell the causes – When you see the lines of Ignorance; poverty, and disease running nearly parallel – you can easily fortil⁶ the curve of Death before it is even plotted! – All depends on ample and minutely correct registers of Births, Diseases – food – Drink – education – Deaths &c &c – when the list is defective, the results are not satisfactory– – One general rule applies to the Curves – Generally, you take Time for a base – and Number for a perpendicular – Years – months – or distance for a Base – Quantity – or numbers of individuals for the perpendicular – Let us suppose that on a certain day, the census of Dublin City was taken – distinguishing between male & female and the Age of each person was taken; & from that a table of those alive between certain ages viz – between 5 & 15 years – between 16 & 25 &c & – on this data a Table of Ages is constructed – and that we wish to lay down the Curve of life – or A curve for the living – We have nothing to do with Death at Present –

Suppose the Total female population to be 500.000 – say of those there are between the ages of 5 & 15 – 150.000 – and those between the ages of 76 & 85 are = to 70.000 – (It does not signify what scale for the Base & perpendicular you adopt – tis the same in this as Railway Sections, or anything else – the base may be one scale the perpendicular another – The above Table of Ages is made at Random) – You have now 150.000 living, between the ages of 5 & 15 – on your perpendicular scale lay off 150.000 – put a dot in the c^r7 of the proper Column – next you have living between 16 & 25 a number of individuals – 140.000 – lay off on your scale as before 140.000 – in the c^r of column $\frac{6}{\mathrm{\text{25}}}$ – proceed in the same way with all your numbers and ages – the last is $\frac{96}{\mathrm{\text{100}}}$ and upwards – of those at 100 there are living ~14.000 – lay off fourteen thousand in the proper column – Now connect all your points or dots, this will form the curve of life; Female, – Now for the Male curve – Suppose you have 150.000 males alive between the ages of 5 & 15 (that shows that an equal number of Male & Female are born) – lay off as before 150.000 in the column of $\frac{5}{\mathrm{\text{15}}}$ – Next, your return or census shows that there are between the ages of $\frac{\mathrm{\text{16}}}{25}$ a number = 116.000 – lay off 116.000 in the proper column $\frac{\mathrm{\text{16}}}{25}$ – proceed in the same with all the ages down to 86 | to | 95⁸ at this age you find 25.000 alive – Now connect all your points by dots – and this Dotted shows the curve of life for the Males – – Something remarkable in those curves – you see the Male & female are nearly parallel after the age of 16 | to | 25⁹ – at $\frac{\mathrm{\text{16}}}{25}$ an awful difference occurs – We see that at 5 | to | 16¹⁰ there were an equal number of males & females alive – why then should there not be an equal number all through the different ages, & the two lines male & female would be identical – but an awful difference occurs among the population between the ages of 16 & 25 on the Male side – What is the cause of this? Natural death – War – or Emigration? – As yet we cannot tell – But when we come to lay down the curves of Death, those curves will explain all, & show that the difference is owing to death – and the diseases will show the cause of Death – it will show that young men in the city give way at a certain age – give way to intemperance & Debauchery – and that the females escape – hence the difference in the Curves Q.E.D.–!¹¹

I send a Tracing of The Tide wave,¹² taken at Meades Quay Limerick,¹³ the principal difference between this curve & the last I sent, is, that on this tracing the low water is not so rounded as high water, this is perhaps, caused by the narrowing of the channel and rush of the river meeting the Flood Tide – I looked on a map a few days ago, on the place in the C^o. Wexford¹⁴ where the low water is sometimes higher than high water, it is a plain open coast – open to the Sea – and I could not, nor could I find anybody who could give any probable reason for this curious fact

The different colours represent the different days – the whole thing is not well done, but I did it as well as time and the opportunity would permit –

I send you a Tracing of the Shannon,¹⁵ there were 7 Tide gauges placed along the N. side of the River, beginning at Liscanor¹⁶ and ending at Limerick (Meades Quay) the tops of all the gauges were on the same level, made so by the spirit Level, – at each gauge a person was placed, and on a certain day & hour (low water) they entered the heights of the rise in a Book & from those books the Sections were plotted. – No 1. is the mean of many observations – and all you can learn from it is the curious difference that exists between the different Stations – if a mean is taken at one place it would not be on the same level with a mean taken at another place – you see the Tide rises more than a foot higher at Meades Quay Limerick, than it does down at the open sea at Liscanor –

N^o. 2, is one Tide – the perpendicular Scale represents Time and distance – each marks the time of low water at his station, begin at the right and look at the times of high & low water, look along to the right and at each Station you find the time of high and low water differs – all the way to Limerick – (observe the red lines, I dont understand the blue lines) Look along a red line and it will give you the form of the surface of the Sea – the whole length of the Shannon, at a particular hour – say 50 minutes past one – this line differs considerably from that at 20 minutes past 2 – and so forth, indeed by a simple inspection you will see more than I could tell you Whilst I was making the tracing our trusty man was kept on the look out, I ran my pen along the lines – hurridly – so that the thing is by no means so satisfactory as If I had taken a good Copy – I send it merely as affording an insight into the methods used – as mere hints –

H.W. – is high water –

S.p – Spring Tides

N.P – Neap tides

HW. ST – high water Spring Tides

&c &c –

Since I wrote last, I have been getting lessons on the Electrotype – I begin to understand it and am making my first attempt without the assistance of the Master, I think I will succeed – I sent a note on Saturday to M^r Kelly, enclosing one for you,¹⁷ – I will write in a day or two to the Gentleman in Scotland,¹⁸ I don’t know of any person who would Suit him, the Salary is so low – it would not be of any effectual good to write to some one on the O.S. I think they are better as it is – but if you know of one who is out of employment, and would take anything rather than be idle, I would like you to send me his address soon – I think you are in the Country and will not get this letter for some time, therefore I send it to the care of M^r Kelly. I have not heard of you for a long time – write soon after you get this –

Yours truly | A McL.

RI MS JT/1/TYP/11/3826-3829

RI MS JT/8/1/4a