Care Messrs. Morton, Rose & Co.
Bartholomew Lane
E. C. London, England

París
June 6, 1883

Dear Sir

Mr. Chaney is in Paris and expects to remain here for a week or more longer and he says that I could do nothing about the comparisons until his return, and not then unless I bring an official and formal request. I told him I expected to find the official letter from you on my arrival in London. The Hardy’s noddy is not yet complete and therefore I could do neither of my two main pieces of business in England if I were there. It is very hot here and I should be only too glad to escape to England, but my order for the pendulum apparatus has been retarded by several unforeseen

I have discovered a new source of error in determinations of the absolute force of gravity with reversible pendulums resting on tongues. Namely, the tube which forms the stem of the pendulum has to be so much cut away about the knife-edges that a flexure takes place at the heavy end. I have made a mathematical analysis of the case and find that the square of the period of oscillation is altered in the ratio of:

Namely        γ₁=-18             γ₂=200
                       l1=200             l2=18700

And when φ₁ + φ₂ = 3.14      φ₁ - φ₂ = 0.0014

With the "Peirce" pendulums the flexibility is about one half what it is with the Repsold pendulum; moreover the effect on the period is multiplied by a coefficient only ½ as large to give the effect on the length of the seconds pendulum. Still, even with these pendulums, the correction in question is very considerable.

This new point is considered here to be a matter of some importance, and my analysis to be rather skillful. I have written a memoir on the subject which I hope Gen'l Cutts will have the kindness to read and explain at Rome, as it will be subjected to severe criticism, and is destined to influence the conduct of pendulum work very considerably.

Under these circumstances, I have thought that the new apparatus ought

I also want to give an order for an apparatus to measure the pendulums on the principle of end-measures. It will all come into the amount allowed. Please cable if you disapprove, and I will not give the order until you have had time to cable.

You might also cable how much you want the total of my vouchers (exclusive of pay) to amount to for June. I can thus make a payment if desired

I will write to Messrs. Morton, Rose and Co., London, notifying them that any telegram sent through Messrs. Morton, Bliss & Co., New York, addressed Peirce is for me. You can then cable 1st 'Peirce', 2nd the number of hundred dollars my June vouchers are to come to, 3rd Yes or No, according as my order already given to Gautier is approved or not, 5th Yes or No, according as the order for a measuring apparatus not to exceed $650 is accepted or not. Of course I shall save all I possibly can on it because I want authorization for a vacuum chamber, which is an essential part of an invariable pendulum. The new pendulums will be invariable enough for Herschel himself, I think; as the knives can only be interchanged

I expect to leave Paris Monday night.

Yours respectfully,

C. S. Peirce
Assist.