center does not turn when the limb is turned, but what is gained here is lost in the accuracy of graduation, as they created two different and distinct centers for both limb and vernier. If these instruments are made very good they will stand a test that would seem absurd in the old style of construction. This test is to clamp limb and vernier together and set to zero and read both verniers. Now turn both limb and vernier together without touching upper clamp and tangent screw for 45°, 90°, etc., and see if the zero marks always remain together. But be particular that you change your position towards the instrument every time in taking each reading, that is, if you face N. and S. in the first reading, you have to face N. E. and S. W. in the second, E. and W. in the third, and so on. If the instrument had a little rough usage, or if the centers are worn ever so little, that it would make no conceivable difference in the old construction, the verniers will not read the same although the tangent screw is not touched and even you may find one position, perhaps N. and S., where the limb graduation seems to be perfectly concentric by turning the limb and not changing your position against the instrument. These errors are caused because the limb turns on one center and the vernier turns on another one.

The next important feature in transits is the firmness of all clamps and tangent screws, so the limb will not turn while the vernier is turned. To ascertain this a second telescope is sometimes fastened under the limb circle in large instruments.

For limb as well as vernier a clamp surrounding the center and leaving the limb plate perfectly free with a tangent screw working against a strong spiral spring seems to give the best satisfaction. The rims of the limb and vernier circle are mostly connected with the center parts by ribs running like radii to make them as light and strong as possible. The openings of the verniers should be large to admit plenty of light, and provided with an opaque shade. The graduation should be plain with sharp cut black marks, limb and vernier lying in the same plane and absolutely concentric.

The standards should be firm and strong, equidistant from the center and running parallel with the north and south lines of compass. Whenever no compass is needed it would be best

to cast both standards in one piece as is done in larger instruments for astronomical purposes.

The telescope must be at right angles to its axis, whose bearings must be adjustable to make the telescope swing truly vertical. Also for convenience of reversing, both ends of the telescope should swing over the compass box.

The telescope slide should be a perfect fit and the objective so fastened and truly centered that the line of collimation will not change in any position. If our American engineers could get used to the inverting telescope as our European brothers, we could have a more powerful telescope without increasing the present size. The telescope should give a clearly defined, bright view, with enough magnifying power to see objects 1,000 feet away. The extreme magnifying power is often a drawback, as it darkens the view to such a degree that in dark, misty days nothing can be seen.

As to the leveling instruments, most of what is said about the transits will also have reference to this class of instruments. In the first place, the base or tripod should be rather more firm yet than in transits, owing to the more sensitive level vial used in levels. The center should be strong and of sufficient length to be absolutely firm, it should be as near to the tripol head as possible. The level bar bearing the Ys should be strong and rigid, of hard metal to keep its shape under various conditions. The old way of separating the level bar from the center is objectionable because it increases the distance of the bar from the center; any looseness of center will be more perceptible and it causes frequent adjustment of the Ys. The closer the telescope to the axis and base of the instrument the firmer it will be; therefore, the Ys should be just high enough to let the telescope with level attached pass over the bar. The telescope itself should be evenly balanced on both sides of the Ys, so that if the telescope is focused for medium distance both ends should be equally heavy. The telescope should not be clamped too hard on the Ys, or it will wear the bearings and require frequent adjustment; its objective head should be light to overcome the unevenness of weight if focused for near and far. The rings upon which the telescope revolves should be of the hardest metal and of absolutely equal diameter.

In closing my remarks I will say that in constructing these. instruments we have to confront two opposing factors. We want the greatest possible strength and firmness, combined with the least weight and greatest portability. To obtain this result the rule is, make as few parts as possible, a piece that can be cast in one is better than two pieces screwed together; the simpler the instrument, the fewer the adjustments, the better for the instrument.

PRESIDENT: Of course I cannot say that all the members are as much interested in this paper as I am. It interests me a great deal. There was one point he did not touch upon, which I have been hammering upon a good many years: The length of the transit axis.

Now suppose there is a little deviation in the position of the transit axis. If it is a short one, by so much is the line of sight the more readily turned out of place, so much more error there will be to the adjustment of the line of sight or the ranging of a straight line.

I see no reason why the limit of the length of the transit axis is not the outside diameter of the plate and I would like to have it made that long. I am also in favor of the three Ys.

Another thing I wish to emphasize, that I don't think Mr. Beckmann has put any too strongly, is the use of the inverting telescope. If we start the objective slide a little, we will have here a focus of seven inches. One may be ranging a line half a mile. You have got hold of seven inches of it. With an inverting telescope there will be no difficulty in placing the cross wires nearer the eye end of the telescope and getting a ten inch grip. That is one use of an inverting telescope. Put the cross wire ring back there; three-fourths of an inch is enough for the eye piece. I have such a telescope and if I break a cross wire all I do is to take out these two screws and put the cross hairs into my instrument without taking the ring out. I haven't got to fuss around again to put those cross wires in. I didn't take them out. But as we were to have this paper on elements of precision, perhaps that is a little out of order.

COL. MUENSCHER: You want the ring put close to the eye

-end. One thing I would like to modify a little. The slow motion of the body of the instrument-the recognized use of the spring. The spring ought to be very strong, or there will be constant motion of the instrument. I have an old instrument and three or four years ago I had occasion to have it repaired, and sent it to Aloe at St. Louis, and he took out one of the pairs of screws and put in a spring, and I never have had any peace with that instrument since. The spring wasn't strong enough.

PRESIDENT: Mr. Beckmann will be glad to fix it for you, no doubt.

MR. STEELE: I feel that we are under obligations to the manufacturers of these fine instruments for coming here and representing their own work, and for sending work here for us to examine, and whatever we may say in regard to them, is done in a spirit of pleasant criticism, for their good, and for our own as well. I think that one of the important things that we have aimed at has been overdone. A light instrument has been attempted, and lightness in all its parts has for some years now been the aim of the manufacturer, and to some extent that has been carried too far. I think I am as lazy a man as any here, and would like to do as little work and get as big pay for it as I could at the same time, but I don't want to do the work over again. When it is once done, I want it done. Now I will call no names, but here is an instrument that you can judge from its general appearance is a fine one. It stands upon a tripod which has been attempted in the line of lightness, and as the maker supposed undoubtedly, strength also, but I consider it faulty, very much so. These pieces are all ash and are dug out on the inside, as you will see here, so that only the shell is left, not as thick as that pencil. These two ribs here are also carved out in various places to reduce their weight. The nuts that go upon these bolts are all loose. They are liable to come off whenever you are least expecting. That should be prevented, and it is done in this other instrument— the only one I have ever seen.

Now, it stands very much to reason that if we have a heavy instrument as this is, upon a light tripod, any strain will affect the instrument much more than as though we reverse those

conditions. This instrument will shake because there is not as much under it as there should be. Neither is the tripod strong enough to stand the rough usage of the field.

I have tried several instruments, and I have a small one now on a good solid tripod, and last summer it was used by a railroad engineer for a short time, and stood upon a sandy bank where the sun was pouring upon the bank and reflected upon the instrument, and staid there for two hours, and during all that use the very last sight, in coming back and testing each one, came on to the nail where it was first set off. In other words, the effect of the intense heat on that instrument had not changed anything at all. The engineer remarked that he could not do that with any instrument he had ever seen before. It occurred to me that the very fact that it was a light instrument was one reason it was not affected, less liable to be affected by the heat.

This instrument, however, will illustrate also what Mr. Beckmann has told you. You may take your magnifying glass and set at zero and turn it around, and you will find the other side is just one graduation off. You may try it a dozen times and find it so every time. That is a perfect illustration of what Mr. Beckmann has been showing us.

COL. MUENSCHER: That instrument seems to have the same defect Prof. Davis speaks of, having a very short axis. I suppose the shape the standard is put in is with the idea of making the standards steadier, but it seems to me it does not accomplish the object.

NOTES IN A ROLLING-MILL.

E. H. MUMFORD.

There is relatively little understood regarding the momentary work required to roll sheets and bars in the rolling-mill of today. I mean that, while experience has taught engineers the advisable amount of power to supply and the marginal excess of fly-wheel inertia, yet the actual work done on a given pass and the proportion in which this work is shared between